Sampling Distributions AP Statistics

A Gallup Poll asked a random sample of 1240 adults, "Do you play video games?" Suppose the true proportion of all adults who play video games is p = .26.
What is the standard deviation of the sampling distribution of p̂?  Check that the 10% condition is met.

• The 10% condition is met.  σp̂ = .0126

• The 10% condition is not met.

• The 10% condition is met.  σp̂ = .0074

• The 10% condition is met.  σp̂ = .26

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?

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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?

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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%