# (Answered) MATH399N Week 6 Assignment: Confidence Intervals

Question

Michelle, a student studying music, randomly sampled fellow music majors and asked whether they listen to music while they study. The resulting confidence interval for the proportion of music students who listen to music while studying is (0.09,0.26).

What is the margin of error?

# Question

Suppose we know that a confidence interval for a population proportion is (0.572,0.662), with a sample proportion of p′=0.617.

What is the margin of error?

# Question

In Philadelphia, a popular diner for tourists recently added cinnamon buns to their menu. In reviewing the sales for this new menu addition, the diner found the mean orders for cinnamon buns in a random sample of business days was x¯=12 orders, with a margin of error of 2 orders.

Construct a confidence interval for the mean number of cinnamon bun ordered by this diner in one day.

# Question

A technician randomly sampled repair logs for computers at a university. He wanted to find out how many times the computers were repaired. The proportion of computers that were repaired more than three times in the last two years was 0.24, with a margin of error of 0.03.

Construct a confidence interval for the proportion of university computers that were repaired more than three times in the last two years.

# Question

The scores on a standardized test are normally distributed. If a random sample of standardized test scores is taken and the confidence interval is (92.3,120.7), what is the sample mean x¯?

Give just a number for your answer. For example, if you found that the sample mean was 12, you would enter 12.

# Question

Suppose we know that a confidence interval for a population proportion is (0.15,0.19), with a margin of error of 0.02.

What is the sample proportion, p^?

# Question

A random sample of garter snakes were measured and the proportion of snakes that were longer than 20 inches in length recorded. The measurements resulted in a sample proportion of p^=0.25, with a sampling standard deviation of σp^=0.05.

Using the Empirical Rule, write a 68% confidence interval for the true proportion of garter snakes that are over 20 inches in length.

# Question

The average weight of a population of female calico cats is unknown. A random sample of female calico cats selected from the population yields a sample mean of x¯=10.1 pounds. Assume the sampling distribution of the mean has a standard deviation of σx¯=1.6 pounds.

Use the Empirical Rule to construct a 68% confidence interval for the true population mean weight.

# Question

The average family size of a population is unknown. A random sample selected from the population yields a sample mean of x¯=4.6 people. Assume the sampling distribution of the mean has a standard deviation of σx¯=0.9 people.

Use the Empirical Rule to construct a 68% confidence interval for the true population mean family size.

# Question

The average number of pages per book from a library is unknown. A random sample of books from the library yields a sample mean of x¯=149.7 pages. Assume the sampling distribution of the mean has a standard deviation of σx¯=14.1 pages.

Use the Empirical Rule to construct a 99.7% confidence interval for the true population mean number of pages.

# Question

A company sells juice in one-quart bottles. In a quality control test, the company found the mean volume of juice in a random sample of bottles was x¯=31 ounces, with a margin of error of 3 ounces.

Construct a confidence interval for the mean number of ounces of juice bottled by this company.

# Question

A random sample of cellphone users were asked whether they send text messages on their phone. The resulting confidence interval for the proportion of cellphone users who use text messages is (0.68,0.82).

What is the margin of error?

# Question

A random sample of adults in the United States were asked whether football was their favorite sport. The resulting confidence interval for the proportion of U.S. adults who answered “yes” is (0.58,0.72).

What is the sample proportion, p^?

# Question

The weights, in pounds, of the cats in an animal adoption center are normally distributed. If a random sample of cats is taken and the confidence interval is (7.9,12.7), what is the margin of error?

Give a numerical response for your answer. For example, if you found that the margin of error was 2, you would enter 2.

# Question

A random sample of accountants were asked whether they double-check their calculations on a tax form. The resulting confidence interval for the proportion of accountants who double-check their work is (0.89,0.97).

What is the sample proportion, p^?

# Question

An online store sells flower arrangements for birthdays and other special events. In a review of their production costs, the online store found the mean wholesale cost of one shipment of vases was x¯=54 dollars, with a margin of error of 5 dollars.

Construct a confidence interval for the mean cost (in dollars) for one shipment of vases.

# Solution:

Question

Michelle, a student studying music, randomly sampled fellow music majors and asked whether they listen to music while they study. The resulting confidence interval for the proportion of music students who listen to music while studying is (0.09,0.26).

What is the margin of error?

# Question

Suppose we know that a confidence interval for a population proportion is (0.572,0.662), with a sample proportion of p′=0.617.

What is the margin of error?