AP Statistics Sampling Distributions

According to a recent poll, 92% of Americans believe more could be done to end the pandemic. Let's assume this is the parameter value for the population. If you take an SRS of 65 Americans and let p̂ = the proportion in the sample who feel more could be done, is the shape of the sampling distribution of p̂ approximately Normal?

• Yes, because n ≥ 30

• Yes, because np = 59.8

• No, because n(1-p) = 5.2

• No, because 65 ≤ 1/10 N

To find the proportion of students who have taken a COVID test, an SRS of 400 students was taken from an area high school with a population of 1600 students. The statewide proportion of students who have taken a COVID test is p = .48. What is the standard deviation of the sampling distribution?

• .0250

• The Large Counts Condition is not met.

• The 10% Condition is not met.

• .0412

When the mean of a sampling distribution is the same as that of the population, we say that

• it is an unbiased estimator of the population

• it is an unbiased estimator of the statistic

• it is a low variability estimator of the population

• it is a biased estimator of the population

When x̅ differs from sample to sample, we say this is an example of

• variability among the samples

• bias among the samples

• not having large enough sample sizes

• poor survey techniques

The Central Limit Theorem allows us to use Normal distributions to find probabilities involving the sample mean

• when n ≥ 30

• when n ≤ 30

• when np ≤ 10 and n(1-p) ≤ 10

• when the population is 10 times greater than the sample size

• the standard deviation of a population

• the standard deviation of a sample

• the mean of a population

• the mean of a sample

Portly Polls asked 1720 first year college students if they say they like the cafeteria food. According to the colleges, 40% of all first year college students say they like the cafeteria food. What is the probability that Portly Polls' random sample will give a result within 2% of the true value?

• 4.55%

• 95.45%

• 90.9%

• 86.35%

Given a population of values: {1, 2, 3, 4}, create a sampling distribution by finding the mean of all possible samples of size 3. What is compared to μ?

• 
• 
• 
• 

Given a population of values: {1, 2, 3, 4, 5, 6}, create a sampling distribution by finding the mean of all possible samples of size 2. What is compared to μ?

• 
• 
• 
• 

Portly Polls asked 1585 fourth year college students if they still had their original major. According to the colleges, 20% of all fourth year college students still had their original major. What is the probability that Portly Polls' random sample will give a result within 1% of the true value?

• 68.26%

• 15.87%

• 84.13%

• 52.39%