Statistics Quiz Practice Exam!

1. Here are the boxplots of Stats221 Final scores for Provo and Salt Lake Campus:

The interquartile range for SLC is about 20.

True

False

IQR=Q3-Q1=85-65=20

Explanation

IQR=Q3-Q1=85-65=20

2. Here are the boxplots of Stats221 Final scores for Provo and Salt Lake Campus:

T F Both distributions are skewed to the left.

True

False

The "lines" determine the skewness. Since the left lines are longer for Provo and SLC, then they are both left-skewed.

Explanation

The "lines" determine the skewness. Since the left lines are longer for Provo and SLC, then they are both left-skewed.

3. Here are the boxplots of Stats221 Final scores for Provo and Salt Lake Campus:

1. T F Fifty percent of the SLC students scored approximately between 65 and 85.

True

False

50% of the data are between Q1 to Q3.

Explanation

50% of the data are between Q1 to Q3.

4. A Portfolio Manger is interested in studying the effects of some variables on stock returns. Which of the following variables is quantitative?

Zip code

Area code

Industry type

Cash Flow

Cash flow is the only quantitative data.

Explanation

Cash flow is the only quantitative data.

5. What does the standard deviation of a distribution measure?

Shape

Spread

Center

Skewness

Standard deviation measures spread.

Explanation

Standard deviation measures spread.

6. Here are the boxplots of Stats221 Final scores for Provo and Salt Lake Campus:

The proportion of Provo scoring between 62 to 82 is greater than the proportion of SLC scoring between 65 to 85.

True

False

The percentage of the data between Q1 to Q3 is always 50%. SO they are the same.

Explanation

The percentage of the data between Q1 to Q3 is always 50%. SO they are the same.

7. When looking at the histogram below, how do the mean and median compare?

Cannot be determined.

The mean is greater than the median.

The mean is equal to the median.

The mean is less than the median.

The mean is less than the median for left-skewed distribution.

Explanation

The mean is less than the median for left-skewed distribution.

8. The Statistics Department reported that there was a total of 3,215 Stats221 classes that have been offered with a mean enrollment of 55 and a standard deviation of 15. A random sample of 200 Stats221 classes had a mean enrollment of 51 and a standard deviation of 12. What symbols are commonly used to denote these values?

A

B

C

D

mu=population mean
sigma=population standard deviation
x-bar=sample mean
s = sample standard deviation

Explanation

mu=population mean
sigma=population standard deviation
x-bar=sample mean
s = sample standard deviation

9. Consider the following 5-number summary of 120 NBA teams scores:

Which of the following observations in the data set would be called a suspected outlier?

An observation between 85 and 100.

An observation less than 125.

An observation between 70 to 100.

An observation greater than 145

E. There are no suspected outliers in this data set.

Upper Outlier=Q3+1.5(Q3-Q1)=100+1.5(100-70)= 145
Lower Outlier=Q1-1.5(Q3-Q1)=100-1.5(100-70)=25

Explanation

Upper Outlier=Q3+1.5(Q3-Q1)=100+1.5(100-70)= 145
Lower Outlier=Q1-1.5(Q3-Q1)=100-1.5(100-70)=25

10. The mean points of NBA players is 20 points a game with a standard deviation of 5. The mean points for the PBA (Philippine Basketball Association) is 30 with a standard deviation of 10. Wesley scores 22 points a game for the NBA while Doria scores 31 points a game for the PBA. Who has scores the highest in their league?

Wesley

Doria

They have equal scores

Cannot be determined from given information.

Wesley z=(22-20)/5=0.4
Doria z=(31-30)/10= 0.1

The higher the z-score the better the performance.

Explanation

Wesley z=(22-20)/5=0.4
Doria z=(31-30)/10= 0.1

The higher the z-score the better the performance.

11. Refer to the histogram below. It is a frequency histogram of Religiosity among 226 randomly selected college students.

How does the mean and median compared for this distribution?

The mean is less than the median

The mean is equal to the median

The mean is greater than the median

Cannot be determined

Since the histogram shows a left-skewed distribution then the mean is less than the median.

Explanation

Since the histogram shows a left-skewed distribution then the mean is less than the median.

12. Which interval below will contains the most data?

A

B

C

D

E

a. 0%
b. 68%/2=34%
c. 95%/2-25=22.5%
d. 25%
e. 50%

Explanation

a. 0%
b. 68%/2=34%
c. 95%/2-25=22.5%
d. 25%
e. 50%

13. Which of the following graphical displays can be drawn using only the 5 number summary?

Scatterplot

Bar graph

Stemplot

Histogram

Boxplot

boxplot is created from the five-number summary .

Explanation

boxplot is created from the five-number summary .

14.

A researcher wants to know the average dating expenses for BYU single students. The researcher obtained a list of single students from the Records Office who live in the BYU dorms. From this list , 50 students are randomly selected. The 50 students are contacted by phone and the amount they spent on dates are recorded. The average dating expense of the 50 students is $35 with a standard deviation of $8. What is the population of interest?

Average dating expenses of students

All BYU Single students.

The 50 students selected.

All BYU students.

The number of single students who spends between $20 to $50 on date.

Since the study refers to "BYU SIngle Students", then the population is "ALL BYU SIngle Students".

Explanation

Since the study refers to "BYU SIngle Students", then the population is "ALL BYU SIngle Students".

15. Here are the boxplots of Stats221 Final scores for Provo and Salt Lake Campus:

The mean is greater than the median for scores in Provo.

True

False

SInce Provo is left-skewed, then the mean is less than than the median.

Explanation

SInce Provo is left-skewed, then the mean is less than than the median.

16. Which density curve has the smallest standard deviation?

A

B

C

Density "C" has more data closer to the mean, therefore, it has the smallest standard deviation compared to "A" or "B".

Explanation

Density "C" has more data closer to the mean, therefore, it has the smallest standard deviation compared to "A" or "B".

17. A study was conducted using growing rats to examine the effect of jumping height on the strength of bones. Thirty rats were randomly allocated into groups. The first group of rats did low jumps of 30 cm. And the second group of rats did high jumps of 60 cm. After 8 weeks of 10 jumps per day, 5 days per week, the bone density of the rats was measured in mg/cm³. What is the response variable?

Growing rats

Height of jump

Bone density

Age of rat

None of the above.

The response variable in this study is bone density. This is because the study is examining the effect of jumping height on the strength of bones, and bone density is a measure of bone strength. The researchers measured the bone density of the rats after 8 weeks of jumping, which allows them to determine if there is a difference in bone density between the rats that did low jumps and the rats that did high jumps.

Explanation

The response variable in this study is bone density. This is because the study is examining the effect of jumping height on the strength of bones, and bone density is a measure of bone strength. The researchers measured the bone density of the rats after 8 weeks of jumping, which allows them to determine if there is a difference in bone density between the rats that did low jumps and the rats that did high jumps.

18. Here are the boxplots of Stats221 Final scores for Provo and Salt Lake Campus:

The proportion of SLC scoring below 85 is larger than the proportion of Provo scoring below 85.

True

False

For SLC, 75% of the data falls below 85. However, for Provo, greater than 75% of the data falls below 85.

Explanation

For SLC, 75% of the data falls below 85. However, for Provo, greater than 75% of the data falls below 85.

19. A researcher wants to know the average dating expenses for BYU single students. The researcher obtained a list of single students from the Records Office who live in the BYU dorms. From this list , 50 students are randomly selected. The 50 students are contacted by phone and the amount they spent on dates are recorded. The average dating expense of the 50 students is $35 with a standard deviation of $8. A critic of the research project argued that the results lack believability because some single students do not live in BYU dorms. This critic is arguing that the study suffers from

Response bias due to question wording.

Response bias due to interviewer effect.

Under-coverage.

Non-response bias.

Under-coverage occurs when some members of the population cannot be selected as part of the sample.
Non-response is when the survey is not returned.

Explanation

Under-coverage occurs when some members of the population cannot be selected as part of the sample.
Non-response is when the survey is not returned.

20. When should we use a probability sample?

So the sample can be used to make inferences about the population.

Because it is more convenient to use than other types of samples.

So that bias will be eliminated completely from the sample.

So that the sample will perfectly represent the population.

So that sampling variability will be removed.

We use probability sample (SRS, Stratified, Multi-staged) so the sample can be used to make inferences about the population.

Explanation

We use probability sample (SRS, Stratified, Multi-staged) so the sample can be used to make inferences about the population.

21. Which is the BEST graphical method for presenting the distribution of a categorical variable?

Histogram

Stemplot

Boxplot

Bar graph

Pie chart

Bar graph is the BEST graphical method for presenting the distribution of a categorical variable.
Histogram is is the BEST graphical method for presenting the distribution of a quantitative or numerical variable.

Explanation

Bar graph is the BEST graphical method for presenting the distribution of a categorical variable.
Histogram is is the BEST graphical method for presenting the distribution of a quantitative or numerical variable.

22. 1. Consider the following bar chart of Baskepoints sources.

Three of the following statements are correct, one is NOT. Which of the following statements is incorrect?

More points are scored in the 3-pt line than steals.

About 70% of the points come from Free throws and 2-point shots.

Most points come from the 2-point shots.

The distribution is skewed to the left.

Bar graph does not have a shape or distribution because you can re-order the categories and the shape changes.

Explanation

Bar graph does not have a shape or distribution because you can re-order the categories and the shape changes.

23.

Which of the following constitutes a multistage sample 28 elementary school students in the Provo school district?

Obtain a list of all elementary school students in the Provo school district area; assign consecutive numbers to the students on the list; use a random number table to select 28 students from the list.

Obtain a list of all elementary school students from each of the 14 elementary schools in the Provo district; use a random number table to select 2 students from each school.

Randomly select 4 elementary schools in the Provo district; from each of the selected schools randomly select one grade class; from each of the selected classes randomly select 7 students.

Randomly select 4 schools in the Provo district, from each of the selected schools randomly select one grade class; from each of the selected classes randomly select 7 students.

Multi-staged is randomly select from groups, then do SRS to each group selected.
Stratified is to do SRS for every group.

Explanation

Multi-staged is randomly select from groups, then do SRS to each group selected.
Stratified is to do SRS for every group.

24. After a Church game, Jeremiah scored 40 points. His coach, who is a Statistics teacher, told him that the standardized score (z-score) for his points on the game, is 2.5. What is the best interpretation of this standardized score?

Jeremiah’s score is only 2.5

Only 2.5% of the players scored higher than Jeremiah.

Jeremiah’s scoring is 2.5 times the average scoring in the league.

Jeremiah’s scoring is 2.5 standard deviations above the average scoring in the league.

Jeremiah’s scoring is 2.5 points above the average scoring in the league.

z-scores implies the number of standard deviations a particular data is above or below the mean.

Explanation

z-scores implies the number of standard deviations a particular data is above or below the mean.

25. Which one of the following is a FALSE statement about statistical problem solving?

Each step in statistical problem solving can be manipulated either innocently or deliberately to influence people’s opinion.

Determining what should be measured is an important part of question formulation.

Subjects should always be chosen without human subjectivity or bias.

Numbers should always be reported in context

Giving measure of confidence is not necessary when reporting results of statistical inference.

Giving measure of confidence is necessary when reporting results of statistical inference.

Explanation

Giving measure of confidence is necessary when reporting results of statistical inference.

26. A study was conducted using growing rats to examine the effect of jumping height on the strength of bones. Thirty rats were randomly allocated into groups. The first group of rats did low jumps of 30 cm. And the second group of rats did high jumps of 60 cm. After 8 weeks of 10 jumps per day, 5 days per week, the bone density of the rats was measured in mg/cm³. What is the explanatory variable?

Growing rats

Height of jump

Bone density as measured in mg/cubic cm.

Age of rat.

The study is the "effect of jumping height on the strength of bones" The explanatory is the jumping heights and the response is strength of bones measures as bone density.

Explanation

The study is the "effect of jumping height on the strength of bones" The explanatory is the jumping heights and the response is strength of bones measures as bone density.

27. Refer to the histogram below. It is a frequency histogram of Religiosity among 226 randomly selected college students.

Why does the histogram above represent a distribution?

Because the values of Religiosity is from 22 to 62.

Because it shows how Religiosity is a lurking variable

Because values for frequencies are given on the horizontal axis and the bars represent their Religiosity

Because values for Religiosity are given on the horizontal axis and the bars represent their frequencies.

The definition of a histogram is that the x-axis represents the data and the y-axis represents the frequencies of the data.

Explanation

The definition of a histogram is that the x-axis represents the data and the y-axis represents the frequencies of the data.

28. What do we mean when the difference between two treatments, in a comparative experiment, are statistically significant?

Very close to what was expected

So large that there a mistake must have been committed

Due to chance or sampling error

Too large to claim that the difference is due to chance

Definition of Statistical significance: too large to claim that the difference is due to chance

Explanation

Definition of Statistical significance: too large to claim that the difference is due to chance

29. A study measured the Forced Expiratory Volume (FEV, a measure of lung capacity for which higher numbers mean more lung capacity) on several school children ranging in age from 6 to 18. The study also asked the children if the are or have been smokers. Surprisingly the average FEV computed for smokers is higher than the average FEV for non-smokers. Which of the following should we consider when interpreting results from this study:

Since this is an observational study, we can conclude that smoking causes an increase in FEV

Age and height might be lurking variables because older kids will have larger lungs and will be more likely to smoke.

Since this is a designed experiment, we can conclude that smoking causes an increase in FEV

The study results are different from what was expected and therefore we should conclude that there is no relationship between smoking and FEV.

Children should not smoke and therefore the study must be invalid.

Lurking variables affect the response variables but the data have not been verified.

Explanation

Lurking variables affect the response variables but the data have not been verified.

30. Refer to the histogram below. It is a frequency histogram of Religiosity among 226 randomly selected college students.

What is the most reasonable value for Q1, the first quartile, of the 226 religiosity values in the previous question?

28

44

53

56

60

Q1 is the 1/4 of the data. 226/4=57th data.
the 57th data falls in the "42-46" bar by counting the frequencies from the left.

Explanation

Q1 is the 1/4 of the data. 226/4=57th data.
the 57th data falls in the "42-46" bar by counting the frequencies from the left.

31. Below is a back-to-back stemplots of the number of A's in a stats221 class for Provo an SLC for the last 33 semesters:

Which of the following is most correct?

Provo has a higher average and a smaller variability.

Provo has a higher average, but SLC has s smaller variability.

SLC has a higher average and higher variability.

SLC has s higher average, but smaller variability.

Since Provo has more higher data, then it is more variable and higher mean.
The SLC does not have data higher than Provo, therefore, it has less spread and the mean is lower.

Explanation

Since Provo has more higher data, then it is more variable and higher mean.
The SLC does not have data higher than Provo, therefore, it has less spread and the mean is lower.

32. A study was conducted using growing rats to examine the effect of jumping height on the strength of bones. Thirty rats were randomly allocated into groups. The first group of rats did low jumps of 30 cm. And the second group of rats did high jumps of 60 cm. After 8 weeks of 10 jumps per day, 5 days per week, the bone density of the rats was measured in mg/cm³. 22.If a significant difference exists between bone density of the two groups, can we conclude that the height of the jump causes differences in bone density for rats?

No, because the study is an observational study.

No, because of possible bias dues to lack of placebo.

No, because the study was only performed once.

Yes, because the study is a valid experiment.

Yes, because the study is double blind.

Experiment is the only study that can establish causation between explanatory and response variables.

Explanation

Experiment is the only study that can establish causation between explanatory and response variables.

33. A Sunday school teacher records the attendance for the first 10 meetings. A record of the attendance is shown below. 42 46 30 43 43 8 41 40 43 44 Considering the distribution of the data, which value best summarizes the attendance at the Sunday School meetings?

39.5

42.5

43.5

46.5

This data has an outlier, which is 8. Therefore, the median best summarizes this data.

8 30 40 41 42 43 43 43 44 46

Median=(42+43)/2=42.5

Explanation

This data has an outlier, which is 8. Therefore, the median best summarizes this data.

8 30 40 41 42 43 43 43 44 46

Median=(42+43)/2=42.5

34. A financial adviser told you that it is better to invest your money in the stock market than putting it in the bank. Assume that the distribution of stock returns is normal with mean µ=10.05% and standard deviation, σ=12.12% per year. Find the proportion of people who invested in the stock market that get less than 8% return on a typical year.

0.0668

0.3085

0.4325

0.6915

0.4984

z=(8-10.05)/12= -.17

From the Normal Table, the probability to the left of the z-score is 0.4325

Explanation

z=(8-10.05)/12= -.17

From the Normal Table, the probability to the left of the z-score is 0.4325

35. A researcher wants to know whether clean air filter improves gas mileage. 10 vehicles were randomly selected. For each vehicle, a coin is tossed. If it is heads, a clean air filter is installed first in the vehicle and the average mileage is computed. After the testing, a dirty air filter is installed and the average mileage is computed. If it is tails, then a dirty air filter is installed first and then a clean air filter is installed next. This study is an example of

A completely randomized experiment

A randomized block experiment

A matched pairs experiment

An observational study

A multi-stage sample

Matched-pairs is when each subject gets both treatments.

Explanation

Matched-pairs is when each subject gets both treatments.

36. Coach Sloan is wants to know how different feet positions affect shooting field goal percentage. He randomly assigns 30 players to 3 different feet positions. He compares the field goal percentages among the three groups. This study is an example of

A completely randomized experiment

A randomized block experiment

A matched pairs experiment

An observational study

A multi-stage sample

It is a completely randomized experiment.when the subjects are randomly assigned to the treatments.
It is a randomized block when the subjects are separated first by "gender" then each gender is assigned to the treatments.

Explanation

It is a completely randomized experiment.when the subjects are randomly assigned to the treatments.
It is a randomized block when the subjects are separated first by "gender" then each gender is assigned to the treatments.

37. Which of the following is a benefit of a randomized block design compared to a completely randomized design?

Blocking can be used as a substitute for double blinding.

Blocking reduces chance variation by removing variation associated with the blocking variable.

Blocking removes bias created by not randomly allocating individuals to the treatments.

Blocking can be used instead of reproducing the entire experiment in order to estimate chance variation.

benefit of a randomized block design compared to a completely randomized design is Blocking reduces chance variation by removing variation associated with the blocking variable..

Explanation

benefit of a randomized block design compared to a completely randomized design is Blocking reduces chance variation by removing variation associated with the blocking variable..

38. Given a histogram, how will you approximate the standard deviation?

Use the standard deviation formula.

Range divide by 2

Range divide by 4.

Range divide by 6

Cannot be computed.

approximate standard deviation = Range divide by 6

Explanation

approximate standard deviation = Range divide by 6

39. Given the figure below:

If basketballs X, Y, and Z are added to the group of five balls at the left, how will the standard deviation of the volume of the new 8 balls compare with the standard deviation of the volume of the original set of 5? The standard deviation of the volume of the new set of 8 balls will be _________ the standard deviation of the volume of the original 5 balls. Fill in the blank.

Smaller than

The same

Larger than

Cannot be determined from the information given.

Standard deviation decreases when adding data equal to the mean.
Standard deviation increases when adding data above or below the mean.

Explanation

Standard deviation decreases when adding data equal to the mean.
Standard deviation increases when adding data above or below the mean.

40. Consider the following histogram of religiosity of college students. What is the appropriate measure of spread for this distribution?

Mean religiosity

Median religiosity

Standard deviation of religiosity

Interquartile range of religiosity

Range

IQR is the appropriate measure of spread for skewed distributions.
Standard deviation is the appropriate measure of spread for symmetric distributions.

Explanation

IQR is the appropriate measure of spread for skewed distributions.
Standard deviation is the appropriate measure of spread for symmetric distributions.

41. A Sunday school teacher records the attendance for the first 10 meetings. A record of the attendance is shown below. What is the Interquartile Range (IQR)? 42 46 30 43 43 8 41 40 43 44

38

42

43.5

35

3

8 30 40 41 42 | 43 43 43 44 46
Min Median=(42+43)/2=42.5
Q1=40
Q3= 43
IQR=Q3-Q1=43-40=3

Explanation

8 30 40 41 42 | 43 43 43 44 46
Min Median=(42+43)/2=42.5
Q1=40
Q3= 43
IQR=Q3-Q1=43-40=3

42. Coach Sloan is testing a new method of shooting free throws and plans to randomly assign 20 players to the new method 25 players to the traditional method. The mean percentage of free throws will then be compared between these two groups. What type of study is this?

An observational study

A simple random sample

A matched pairs experiment.

A completely randomized experiment.

A randomized block experiment.

It is a completely randomized experiment.when the subjects are randomly assigned to the treatments.
It is a randomized block when the subjects are separated first by "gender" then each gender is assigned to the treatments.

Explanation

It is a completely randomized experiment.when the subjects are randomly assigned to the treatments.
It is a randomized block when the subjects are separated first by "gender" then each gender is assigned to the treatments.

43. There are three portfolio managers in a room who managed money for 10, 15, and 20 years. If a portfolio manager who managed money for 15 years enters the room, what will happen to the mean and standard deviation of the years managing money?

The mean and standard deviation will increase.

The mean and standard deviation will decrease.

The mean and standard deviation will stay the same.

The mean will stay the same but standard deviation will decrease.

The mean will stay the same but standard deviation will increase.

standard deviation decreases when adding the mean.
compute the mean=(10+15+20+15)/4=15, stays the same.

Explanation

standard deviation decreases when adding the mean.
compute the mean=(10+15+20+15)/4=15, stays the same.

44. Refer to the histogram below. It is a frequency histogram of Religiosity among 226 randomly selected college students.

Which of the following is the most reasonable value for the median of the distribution?

28

44

53

56

60

The median is the middle data. There are 226 data, therefore the middle data is 226/2=113th and 114th.

By reading the frequency we can see that the 113th and the 114th data are in the "50-54" bar.

Explanation

The median is the middle data. There are 226 data, therefore the middle data is 226/2=113th and 114th.

By reading the frequency we can see that the 113th and the 114th data are in the "50-54" bar.

45. A financial adviser told you that it is better to invest your money in the stock market than putting it in the bank. Assume that the distribution of stock returns is normal with a mean of 10.05% and a standard deviation of 12.12% per year. You want to invest in a strategy that results in the highest 4% of the returns. Thus you will select an investment with a return higher than ________.

20.1

25.7

31.26

40.26

Cannot be calculated.

x = mu + z*sigma
From the Normal Table, z=1.75 has 96% to the left.
x=10.10 + (1.75)(12.12)= 31.26

Explanation

x = mu + z*sigma
From the Normal Table, z=1.75 has 96% to the left.
x=10.10 + (1.75)(12.12)= 31.26

46. A researcher wants to determine if the singles students at BYU would be interested in participating in the compatibility service to be provided by the BYU student services. From a list of BYU single students, the researcher contacted an SRS of 200 and asked them if they would be interested in participating in the compatibility service to be provided by the BYU student services. A total of 50 students said yes. What is the sample in this survey?

All BYU single students

All students in BYU.

The 200 students who were contacted.

The 50 respondents who said yes.

200 were "asked" which implies that they have responded, therefore, the sample is 200.

Explanation

200 were "asked" which implies that they have responded, therefore, the sample is 200.

47. The NBA scores are normally distributed. Approximately what percent of these scores will fall between one standard deviation below the mean and two standard deviations above the mean?

48%

61%

68%

82%

95%

1 standard deviation below the mean is 68%/2=34%.
2 standard deviations above the mean=95%/2=47.5
34% + 47.5% = 81.5% or 82%

Explanation

1 standard deviation below the mean is 68%/2=34%.
2 standard deviations above the mean=95%/2=47.5
34% + 47.5% = 81.5% or 82%

48.

In order to assess opinions of BYU single students about the stated curfew regulation, a random sample of BYU single students were selected from each Singles Ward in BYU. What type of sample is this?

Simple random Sample

Stratified random sample

Multistage sample

Completely Randomized experiment

Randomized Block Design

Multi-staged is randomly select from groups, then do SRS to each group selected.
Stratified is to do SRS for every group.

Explanation

Multi-staged is randomly select from groups, then do SRS to each group selected.
Stratified is to do SRS for every group.

49. Here are the boxplots of Stats221 Final scores for Provo and Salt Lake Campus:

1. T F Scores exhibit less spread for Provo than SLC.

True

False

Spread is measured by the IQR=Q3-Q1 or the length of the box. Since the length of the box for Provo and SLC are equal, therefore, they have the same spread.

Explanation

Spread is measured by the IQR=Q3-Q1 or the length of the box. Since the length of the box for Provo and SLC are equal, therefore, they have the same spread.

50. Church League scoring follows a normal distribution with 16% of the scores greater than 41.4 and 16% less than 38.8. What is the standard deviation for these scores?

1.3

2.3

3.4

4.3

"16% of the scores greater than 41.4 and 16% less than 38.8." implies that 68% of the data is between 41.4 and 38.8.
From the Empirical rule (68-95-99.7), we can conclude that 68% of the data is between 1 standard deviatio abobve the mean and one standard deviation below the mean, for a total of 2 standard deviations.

Therefore, standard deviation = (41.4-38.8)/2=1.3

Explanation

"16% of the scores greater than 41.4 and 16% less than 38.8." implies that 68% of the data is between 41.4 and 38.8.
From the Empirical rule (68-95-99.7), we can conclude that 68% of the data is between 1 standard deviatio abobve the mean and one standard deviation below the mean, for a total of 2 standard deviations.

Therefore, standard deviation = (41.4-38.8)/2=1.3

51. A financial adviser told you that it is better to invest your money in the stock market than putting it in the bank. Assume that the distribution of stock returns is normal with a mean of 10.05% and a standard deviation of 12.12% per year. Find the proportion of people who invested in the stock market that get more than 20% return on a typical year.

0.0994

0.0735

0.2061

0.7939

None of the above.

z=(20-10.05)/12.12=0.82
From the Normal Table, the percentage to the left of z=0.82 is 0.7939
The percentage to the right is 1 - 0.7939 = 0.2061

Explanation

z=(20-10.05)/12.12=0.82
From the Normal Table, the percentage to the left of z=0.82 is 0.7939
The percentage to the right is 1 - 0.7939 = 0.2061

52. Refer to the histogram below. It is a frequency histogram of Religiosity among 226 randomly selected college students.

What is the rough estimate of the standard deviation of the above histogram?

1

3

5

7

9

estimate of standard deviation=range/6=(max-min)/6=(62-22)/6=6.7 or 7

Explanation

estimate of standard deviation=range/6=(max-min)/6=(62-22)/6=6.7 or 7

53. To investigate the effects of playing basketball, 100 men in the 40-50 age range who play basketball were located. Also, 100 men of the same age and weight ranges, who had never played basketball, were located. The incidence of constipation was compared between the two groups. What kind of study is this?

A multi-staged sample

A simple random sample

A completely randomized experiment

A matched pairs experiment

An observational study

This is only an observational study because we are not "forcing" the subjects to the treatments. We are only "observing".

Explanation

This is only an observational study because we are not "forcing" the subjects to the treatments. We are only "observing".

54. A financial adviser told you that it is better to invest your money in the stock market than putting it in the bank. Assume that the distribution of stock returns is normal with a mean of 10.05% and a standard deviation of 12.12% per year. Find the proportion of people who invested in the stock market that get between 8 to 11% return on a typical year.

0.0994

0.0735

0.3651

0.6349

Cannot be calculated.

z=(8-10.05)/12.12= -0.17
z=(11-10.05)/12.12= 0.08

From the Normal Table,
the percentage to the left of z=0.08 is 0.5319
the percentage to the left of z= -.17 is 0.4325
the percentage between the z-scores is =.5319 - 0.4325 = 0.0994

Explanation

z=(8-10.05)/12.12= -0.17
z=(11-10.05)/12.12= 0.08

From the Normal Table,
the percentage to the left of z=0.08 is 0.5319
the percentage to the left of z= -.17 is 0.4325
the percentage between the z-scores is =.5319 - 0.4325 = 0.0994

55. A researcher wants to determine if the singles students at BYU would be interested in participating in the compatibility service to be provided by the BYU student services. From a list of BYU single students, the researcher selects an SRS of 200 and mails a brief questionnaire addressed to a single student address. A total of 50 questionnaires are returned. What is the chance that all 200 BYU single students came from BYU 215 Ward ?

Exactly zero because an SRS will contain addresses from all BYU singles students from different wards

Reasonably larger due to sampling variability.

200 divided by the size of the population of BYU single students.

The same as for any other set of 200 BYU single students.

Cannot be computed.

DEfinition of SRS: the same chance of being selected for any size n.

Explanation

DEfinition of SRS: the same chance of being selected for any size n.

56. According to the NBA rules, a basketball is supposed to weigh between 20 to 22 ounces. Basketball produced by Spalding on one production line has a mean of 21.3 ounces and a standard deviation of 0.3 ounces. The weights of this basketball are approximately Normally distributed. Above what weight are 90% of the basketball balls?

21.92

20.92

22.92

None of the above.

x = mu + z*sigma
From the Normal table, the z-score that has .10 to the left of it is z= -1.28

x =21.3+(-1.28)*(0.3)=20.92

Explanation

x = mu + z*sigma
From the Normal table, the z-score that has .10 to the left of it is z= -1.28

x =21.3+(-1.28)*(0.3)=20.92

57. According to the NBA rules, a basketball is supposed to weigh between 20 to 22 ounces. Basketball produced by Spalding on one production line has a mean of 21.3 ounces and a standard deviation of 0.3 ounces. The weights of this basketball are approximately Normally distributed. What proportion of the ball produced on this production line meets the standard weight of the balls?

0.9901

0.0406

0.9954

0.9945

None of the above.

z=(20-21.3)/0.3=-4.33
z=(22-21.3)/0.3= 2.33
From the Normal Table, the percentage to the left of z=2.33 is 0.9901
The percentage to the left of z=-4.33 is 0 because it is outside the range.

So the percentage between 20 to 22 is .9593 - 0 = 0.9593

Explanation

z=(20-21.3)/0.3=-4.33
z=(22-21.3)/0.3= 2.33
From the Normal Table, the percentage to the left of z=2.33 is 0.9901
The percentage to the left of z=-4.33 is 0 because it is outside the range.

So the percentage between 20 to 22 is .9593 - 0 = 0.9593

58. Refer to the histogram below. It is a frequency histogram of Religiosity among 226 randomly selected college students.

What is the appropriate measure of spread for the distribution of religiosity in the above problem?

Mean religiosity

Median religiosity

Standard deviation of religiosity

IQR of religiosity

IQR is the appropriate measure of spread for skewed distribution.

Explanation

IQR is the appropriate measure of spread for skewed distribution.

59. A Sunday school teacher records the attendance for the first 10 meetings. A record of the attendance is shown below. Which measure of center best summarizes the attendance at the Sunday School class? 42 46 30 43 43 8 41 40 43 44

35

43

43.5

41.5

42.5

8 30 40 41 43 43 43 44 46

The middle data is 43.

Explanation

8 30 40 41 43 43 43 44 46

The middle data is 43.