Unit 5 · Test

Unit 5 test: Sampling Distributions

13 questions. Answer them all, then submit to see your score. Solutions unlock after you submit.

This test covers parameters and statistics, sampling variability and bias, the sampling distributions of $\hat{p}$ and $\bar{x}$ , the central limit theorem, and sampling distributions of differences. Give probabilities to four decimal places. This excerpt of the standard normal table may help.

$z$	$-2.00$	$-1.50$	$-1.00$	$1.00$	$1.25$	$1.50$	$2.00$
Area to the left	$0.0228$	$0.0668$	$0.1587$	$0.8413$	$0.8944$	$0.9332$	$0.9772$

Question 1

A national survey of 1,500 randomly selected teenagers finds that 64% have used a certain app in the past week. Which statement is correct?

Question 2

A researcher increases the size of her simple random sample from 100 to 900. What happens to the sampling distribution of $\bar{x}$ ?

Question 3

With a random sample of 50, the standard deviation of a sample proportion is about 0.07. What sample size would make this standard deviation about half as large?

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 4

In a large population, 90% of adults own a smartphone. For random samples of 100 adults, find the standard deviation of the sampling distribution of $\hat{p}$ .

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 5

A school has 500 students, and 30% of them play a sport. A random sample of 40 students is selected without replacement. Which conditions for a normal model of $\hat{p}$ are met?

Question 6

In a large county, 25% of registered voters are under 35. A random sample of 300 registered voters is selected. Find the probability that more than 30% of the sample is under 35.

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 7

The weights of packages handled by a shipping company have standard deviation $\sigma = 24$ ounces. For random samples of 16 packages, find the standard deviation of the sampling distribution of $\bar{x}$ , in ounces.

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 8

The weights of those packages are normally distributed with mean 200 ounces and standard deviation 24 ounces. For a random sample of 16 packages, find the probability that the sample mean weight is less than 191 ounces.

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 9

The number of minutes students spend on homework each night is strongly right-skewed. In which situation is a normal model for the sampling distribution of $\bar{x}$ most appropriate?

Question 10

The number of text messages adults send per day in a large city is right-skewed with mean 12 and standard deviation 5. A random sample of 100 adults is selected. Find the probability that the sample mean is between 11.5 and 13.

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 11

An elevator's sensor warns when the total weight of cargo boxes exceeds 1,531.25 pounds. Box weights have mean 30 pounds and standard deviation 7 pounds, and their distribution is skewed. For a random sample of 49 boxes, find the probability that the total weight exceeds 1,531.25 pounds.

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 12

At a large company, 45% of employees in the sales division and 15% of employees in the research division work remotely at least one day a week. Independent random samples of 150 employees are taken from each division. Find the probability that $\hat{p}_{\text{sales}} - \hat{p}_{\text{research}}$ is less than 0.20.

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 13

Two normal populations have $\mu_1 = 60$ , $\sigma_1 = 12$ and $\mu_2 = 55$ , $\sigma_2 = 9$ . Independent random samples of size 9 are taken from each. Which describes the sampling distribution of $\bar{x}_1 - \bar{x}_2$ ?