# Sampling Distribution Model Quiz Questions

10 Questions | Attempts: 715  Settings  • 1.
A realtor has been told that 42% of homeowners in a city prefer to have a finished basement.  She surveys a group of 400 homeowners randomly chosen from her client list.  Find the mean of the proportion of homeowners in this sample who prefer a finished basement.
• A.

μ = 42%

• B.

μ = 2.5%

• C.

μ = 0.42%

• D.

μ = 58%

• E.

μ = 1.2%

• 2.
A restaurant's receipts show that the cost of customers' dinners has a skewed distribution with a mean of \$54 and a standard deviation of \$18.  What is the probability that the next 100 customers will spend an average of at least \$50 on dinner? Find the specified probability, from a table of Normal probabilities. Assume that the necessary conditions and assumptions are met.
• A.

0.5879

• B.

0.0132

• C.

0.9868

• D.

0.4121

• E.

0.9614

• 3.
Which of the following describe how the sampling distribution model for the sample mean changes as the sample size is increased?   A: The sampling distribution model becomes more Normal in shape B: The standard deviation of the sampling distribution gets smaller C: The mean of the sampling distribution gets smaller
• A.

A only

• B.

B and C

• C.

B only

• D.

A, B, and C

• E.

A and B

• 4.
A certain population is strongly skewed to the left. We want to estimate its mean, so we collect a sample. Which should be true if we use a large sample rather than a small one? I. The distribution of our sample data will be more clearly skewed to the left. II. The sampling model of the sample means will be more skewed to the left. III. The variability of the sample means will greater.
• A.

III only

• B.

I and III only

• C.

II only

• D.

I only

• E.

II and III only

• 5.
A certain population is strongly skewed to the right. We want to estimate its mean, so we will collect a sample. Which should be true if we use a large sample rather than a small one? I. The distribution of our sample data will be closer to normal. II. The sampling model of the sample means will be closer to normal. III. The variability of the sample means will be greater.
• A.

I and III only

• B.

II only

• C.

II and III only

• D.

III only

• E.

I only

• 6.
A sample is chosen randomly from a population that was strongly skewed to the right.  Describe the sampling distribution model for the sample mean if the sample size is small.
• A.

Normal, center at μ, standard deviation sqrt(σ/n)

• B.

Skewed right, center at μ, standard deviation sqrt(σ/n)

• C.

Skewed right, center at μ, standard deviation σ/sqrt(n)

• D.

Normal, center at μ, standard deviation σ/sqrt(n)

• E.

There is not enough information to describe the sampling distribution model.

• 7.
The mean annual income for women in one city is \$28,520 and the standard deviation of the incomes is \$5600.  The distribution of incomes is skewed to the right. Suppose a sample of 12 women is selected at random from the city and the mean income,   is determined for the women in the sample. May the Normal model be used to describe the sampling distribution of the mean,  ?
• A.

No, Normal model may not be used: 10% condition is not satisfied since the 12 women in the sample represent less than 10% of women in the city

• B.

No, Normal model may not be used: Independence assumption is not satisfied: since the women in the sample may live in the same neighborhood, the chance of picking a woman with a high income depends on who has already been selected.

• C.

Yes, Normal model may be used. Randomization condition: The women were selected at random Independence assumption: It is reasonable to think that incomes of randomly selected women are mutually independent. Large enough sample condition: a sample of 12 is large enough for the Central Limit Theorem to apply 10% condition is satisfied since the 12 women in the sample certainly represent less than 10% of women in the city

• D.

No, Normal model may not be used: Large enough sample condition is not satisfied: since the distribution of incomes in the original population is skewed, a sample of 12 is not large enough

• E.

No, Normal model may not be used since incomes of women in the city are not normally distributed but are skewed to the right

• 8.
Assume that 15% of students at a university wear contact lenses. We randomly pick 200 students. What is the standard deviation of the proportion of students in this group who may wear contact lenses?
• A.

σ = 2.74%

• B.

σ = 6.38%

• C.

σ = 5.48%

• D.

σ = 2.52%

• E.

σ = 5.05%

• 9.
When a truckload of oranges arrives at a packing plant, a random sample of 125 is selected and examined.  The whole truckload will be rejected if more than 8% of the sample is unsatisfactory.  Suppose that in fact 9% of the oranges on the truck do not meet the desired standard.  What's the probability that the shipment will be accepted anyway?
• A.

0.6517

• B.

0.3483

• C.

0.6966

• D.

0.7803

• E.

0.2197

• 10.
A health worker believes that 10% of students at a certain college suffer from depression.  She sets up a booth outside the student union building and selects 100 students at random from those leaving the building.  She asks the selected students to complete a questionnaire. May the Normal model be used to describe the distribution of the proportion of students in the sample who suffer from depression? The college has roughly 7000 students.
• A.

Normal model may be used to describe distribution of sample proportions. Randomization condition is satisfied: the students were selected at random and are therefore representative of all students at the college 10% condition is satisfied: the 100 students are less than 10% of all students at the college Success/failure condition is satisfed: np = 10 and nq = 90 are both greater than 10.

• B.

Normal model may not be used to describe distribution of sample proportions. Randomization condition is not satisfied: the students were selected at random but only from those students leaving the student union building, not from the whole student body. Those leaving the student union building may not be representative of all students at the college - those suffering from depression are more likely to stay in their rooms and may not be out as much, participating in activities at the student union building.

• C.

Normal model may not be used to describe distribution of sample proportions. Success/failure condition is not satisfed: np = 10 and nq = 90 are both greater than 10.

• D.

Normal model may not be used to describe distribution of sample proportions. Distribution of population is not normal

• E.

Normal model may not be used to describe distribution of sample proportions. 10% condition is not satisfied: the 100 students are less than 10% of all students at the college

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