Exam 8: Confidence Intervals for One Population Mean

Solve the problem. -Based on a sample of size 41, a 95% confidence interval for the mean score of all students, $\mu _ { ,}$ on an aptitude test is from 60 to 66. Find the margin of error.

Write the word or phrase that best completes each statement or answers the question. -A psychologist wishes to estimate the mean IQ of students at one college. He picks a random sample of 49 students from the college, measures each student's IQ, and obtains the following $95 \%$ confidence interval for the population mean, $\mu : 115$ to 125 . How would you interpret this confidence interval?

Write the word or phrase that best completes each statement or answers the question. -Under what conditions would you choose to use the t-interval procedure instead of the z-interval procedure in order to obtain a confidence interval for a population mean? What conditions must be satisfied in order to use the t-interval procedure?

Find the confidence interval specified. Assume that the population is normally distributed. -A laboratory tested twelve chicken eggs and found that the mean amount of cholesterol was 188 milligrams with s = 12.7 milligrams. Construct a 95% confidence interval for the true mean Cholesterol content of all such eggs.

Find the requested confidence interval. -A college statistics professor has office hours from 9:00 A.M. to 10:30 A.M. daily. A sample of waiting times to see the professor (in minutes) is 10, 12, 20, 15, 17, 10, 30, 28, 35, 28, 19, 27, 25, 22, 33, $37,14,21,20$ , 23. Assuming $\sigma = 7.84$ , find the $95.44 \%$ confidence interval for the population mean.

Find the confidence interval specified. -49 packages are randomly selected from packages received by a parcel service. The sample has a mean weight of 11.7 pounds. Assume that $\sigma$ = 3.1 pounds. What is the 95% confidence interval for The true mean weight, µ, of all packages received by the parcel service?

Provide an appropriate response. -Suppose you have obtained a confidence interval for µ, but wish to obtain a greater degree of precision. Which of the following would result in a narrower confidence interval? A. Increasing the sample size while keeping the confidence level fixed B. Decreasing the sample size while keeping the confidence level fixed C. Increasing the confidence level while keeping the sample size fixed D. Decreasing the confidence level while keeping the sample size fixed

Write the word or phrase that best completes each statement or answers the question. -Define margin of error. Explain the relation between the confidence interval and the margin of error. Suppose a confidence interval is $9.65 < \mu < 11.35$ . Find the sample mean $\bar { x }$ and the margin of error $E$ .

Solve the problem. -A confidence interval for a population mean, µ, has l $\mu _ { ,}$ ength 179.1. Find the margin of error.

Find the confidence level that corresponds to a value of α of 0.12.

Find the confidence interval specified. -A random sample of 149 full-grown lobsters had a mean weight of 15 ounces. Assume that $\sigma$ = 3.6 ounces. Construct a 95% confidence interval for the population mean $\mu .$

Find the confidence interval specified. -A random sample of 110 light bulbs had a mean life of $\bar { x } = 595$ hours. Assume that $\sigma = 31$ hours. Construct a $90 \%$ confidence interval for the mean life, $\mu$ , of all light bulbs of this type.

Find the confidence interval specified. Assume that the population is normally distributed. -A sociologist develops a test to measure attitudes about public transportation, and 27 randomly selected subjects are given the test. Their mean score is 76.2 and their standard deviation is 21.4. Construct the 95% confidence interval for the mean score of all such subjects.

Provide an appropriate response. -In stating a confidence-interval estimate of a population mean, the level of confidence increases as the size of the interval .

Find the specified t-value. -For a t-curve with $d f = 11$ , find ${ } { t } _{0.10} { \text {. } }$

Provide an appropriate response. -In which of the following situations is it reasonable to use the z-interval procedure to obtain a confidence interval for the population mean? Assume that the population standard deviation is Known. A. $\mathrm { n } = 10$ , the data contain no outliers, the variable under consideration is not normally distributed. B. $\mathrm { n } = 10$ , the variable under consideration is normally distributed. C. $\mathrm { n } = 18$ , the data contain no outliers, the variable under consideration is far from being normally distributed. D. $\mathrm { n } = 18$ , the data contain outliers, the variable under consideration is normally distributed.

Write the word or phrase that best completes each statement or answers the question. -Mary wishes to estimate the mean height of women aged 18-24. She picks a sample of 100 women aged between 18 and 24 and constructs a 99% confidence interval for the population mean. If she were to repeat this procedure 200 times in total, she would obtain 200 different confidence intervals. How many of these intervals would you expect to contain the population mean, $\mu ?$ Explain your thinking.

Find the confidence interval specified. -Physiologists often use the forced vital capacity as a way to assess a person's ability to move air in and out of their lungs. A researcher wishes to estimate the forced vital capacity of people suffering From asthma. A random sample of 15 asthmatics yields the following data on forced vital capacity, In liters. 5.1 4.9 4.7 3.1 4.3 3.7 3.7 4.3 3.5 5.2 3.2 3.5 4.8 4.0 5.1 Use the data to obtain a $95.44 \%$ confidence interval for the mean forced vital capacity for all asthmatics. Assume that $\sigma = 0.7$ .

Given that the confidence level is $x \%$ , give an expression in terms of $x$ for $\alpha$ .

Solve the problem. -A sample of 71 college students yields a mean annual income of $\$ 3595$ . Assuming that $\sigma = \$ 898$ , find the margin of error in estimating $\mu$ at the $99 \%$ level of confidence.