Using Sample Data To Estimate Population Parameters Quiz

1) A random sample of 40 students shows that 14 prefer studying in the morning. What is the best estimate of the proportion of all students who prefer morning study?

0.35

0.25

0.30

0.45

Sample proportion = 14 ÷ 40 = 0.35.

Explanation

Sample proportion = 14 ÷ 40 = 0.35.

2) A poll of 500 residents finds that 315 support a new park. What is the estimated population proportion in support?

0.53

0.63

0.68

0.73

Proportion = 315 ÷ 500 = 0.63.

Explanation

Proportion = 315 ÷ 500 = 0.63.

3) A random sample of 60 light bulbs has a mean lifetime of 1,180 hours with a margin of error of ±40 hours (95% confidence). Which is the best interpretation?

The population mean is exactly 1,180 hours.

The population mean is likely between 1,140 and 1,220 hours.

The sample mean will always be within 40 hours of the population mean.

95% of bulbs last between 1,140 and 1,220 hours.

Mean ± MOE = 1,180 ± 40 → range 1,140 to 1,220 hours for the population mean.

Explanation

Mean ± MOE = 1,180 ± 40 → range 1,140 to 1,220 hours for the population mean.

4) Two samples are taken from the same population: Sample A (n=50), Sample B (n=200). Which statement is most likely true?

Both have the same margin of error.

Sample A produces a smaller margin of error.

Sample B produces a smaller margin of error.

Neither can estimate the population.

A larger sample size (200) gives a smaller margin of error.

Explanation

A larger sample size (200) gives a smaller margin of error.

5) In a school of 1,200 students, a random sample of 80 has an average of 2.6 extracurriculars per student. What is this 2.6 best described as?

Sample statistic

Population parameter

Margin of error

Confidence level

2.6 is calculated from the sample, so it’s a sample statistic.

Explanation

2.6 is calculated from the sample, so it’s a sample statistic.

6) What is the best point estimate of the population mean sugar content?

1.6 g

10.1 g

10.5 g

9.8 g

The sample mean (9.8 g) is the best point estimate of the population mean.

Explanation

The sample mean (9.8 g) is the best point estimate of the population mean.

7) What is the 95% confidence interval for the population mean?

9.2 g to 10.4 g

9.4 g to 10.2 g

9.5 g to 10.1 g

9.8 g to 11.4 g

Mean ± MOE = 9.8 ± 0.3 → 9.5 to 10.1 g.

Explanation

Mean ± MOE = 9.8 ± 0.3 → 9.5 to 10.1 g.

8) Based on the interval and the target specification, which conclusion is most reasonable?

The target is definitely violated.

No conclusion is possible with a sample of 100.

The target is met only if the sample standard deviation is under 1.0 g.

The target is likely met since the interval is below 10.5 g.

The whole interval 9.5–10.1 is below 10.5, so the target mean ≤ 10.5 is likely met.

Explanation

The whole interval 9.5–10.1 is below 10.5, so the target mean ≤ 10.5 is likely met.

9) If the nutritionist wants a smaller margin of error at the same confidence, which is the best strategy?

Increase the sample size.

Use a smaller random sample.

Increase the confidence level.

Reduce the sample standard deviation by removing outliers only.

To shrink MOE, you usually need a larger sample size.

Explanation

To shrink MOE, you usually need a larger sample size.

10) A store manager samples 120 receipts and finds the mean purchase is $24.50 with a 95% margin of error of ±$3.00. What is the estimated range for the population mean purchase?

$20.50 to $24.50

$24.00 to $25.00

$21.50 to $27.50

$23.50 to $25.50

24.50 ± 3.00 → $21.50 to $27.50.

Explanation

24.50 ± 3.00 → $21.50 to $27.50.

11) A class surveys 40 households and finds a sample mean of 2.3 pets per household. If the town has 8,000 households, what is the estimated total number of pets?

4,600

2,300

800

18,400

Estimated total = 2.3 × 8,000 = 18,400.

Explanation

Estimated total = 2.3 × 8,000 = 18,400.

12) Which sample size generally yields the smallest margin of error when estimating a population proportion, all else equal?

N = 50

N = 1,000

N = 250

N = 100

Larger n gives smaller MOE.

Explanation

Larger n gives smaller MOE.

13) Which school’s estimate is most precise for its population?

School C

School B

School A

All are equally precise

School C has the smallest MOE (±0.04), so it’s most precise.

Explanation

School C has the smallest MOE (±0.04), so it’s most precise.

14) What is the 95% confidence interval for School B’s proportion?

0.26 to 0.50

0.32 to 0.44

0.34 to 0.40

0.38 to 0.44

Proportion ± MOE = 0.38 ± 0.06 → 0.32 to 0.44.

Explanation

Proportion ± MOE = 0.38 ± 0.06 → 0.32 to 0.44.

15) If the district wants a districtwide estimate, which approach is most appropriate?

Use only School A since it has the highest proportion.

Use only School C since it has the biggest sample.

Combine data from all three schools using appropriate weighting by sample size.

Average the three sample proportions without weighting.

Combine all data, weighting by sample size.

Explanation

Combine all data, weighting by sample size.

16) Which statement is most consistent with the reported MOEs?

School A’s true proportion must be larger than School C’s.

The true district proportion could plausibly be between about 0.32 and 0.40.

School B and School C cannot have overlapping intervals.

The MOEs imply School C’s sample had zero variability.

All three intervals overlap around 0.32–0.40, so district value could be there.

Explanation

All three intervals overlap around 0.32–0.40, so district value could be there.

17) A biologist samples 64 plants and finds a mean height of 28.4 cm with a standard deviation of 4.8 cm. Which change most reliably reduces the margin of error at the same confidence?

Use a higher confidence level.

Remove observations below 20 cm.

Round all measurements to the nearest centimeter.

Increase the sample size.

Increasing sample size reliably reduces MOE.

Explanation

Increasing sample size reliably reduces MOE.

18) In a sample of 150 gym members, 102 report visiting at least three times per week. What is the sample proportion?

0.68

0.62

0.70

0.75

Proportion = 102 ÷ 150 = 0.68.

Explanation

Proportion = 102 ÷ 150 = 0.68.

19) A researcher’s estimate of a population mean has MOE ±5 based on n = 100. To cut the MOE to ±2.5 at the same confidence, approximately what sample size is needed?

N = 150

N = 200

N = 400

N = 1,000

To halve MOE, sample size must quadruple → 400.

Explanation

To halve MOE, sample size must quadruple → 400.

20) A survey of 75 voters finds 39 support Proposition X. The 95% MOE is ±0.11. A headline says “Majority supports Proposition X.” Which best evaluates this claim?

Definitely true because 39/75 exceeds 0.50.

False because 75 is too small to estimate a proportion.

True only if the population is under 10,000.

Uncertain: the confidence interval around 0.52 includes values near or below 0.50.

CI = 0.52 ± 0.11 includes values below 0.50, so majority is uncertain.

Explanation

CI = 0.52 ± 0.11 includes values below 0.50, so majority is uncertain.