Which of the following statements about the sampling distribution of the sample mean is incorrect?

As the sample size gets larger, the standard error of the sampling distribution of the sample mean gets larger as well.

The Central Limit Theorem guarantees that the population is normal whenever n is sufficiently large.

A study was conducted to determine what proportion of all college students considered themselves as full-time students. A random sample of 300 college students was selected and 210 of the students responded that they considered themselves full-time students. Which of the following would represent the target parameter of interest?

What is the confidence level of the following confidence interval for μ? $$\overline{x}\pm2.33\left(\frac{\sigma}{\sqrt{n}}\right)$$

A 90% confidence interval for the mean percentage of airline reservations being canceled on the day of the flight is (1.1%, 3.2%). What is the point estimator of the mean percentage of reservations that are canceled on the day of the flight?

The real estate industry claims that it is the best and most effective system to market residential real estate. A survey of randomly selected home sellers in Illinois found that a 95% confidence interval for the proportion of homes that are sold by a real estate agent is 69% to 81%. Interpret the interval in this context.

The real estate industry claims that it is the best and most effective system to market residential real estate. A survey of randomly selected home sellers in Illinois found that a 99% confidence interval for the proportion of homes that are sold by a real estate agent is 70% to 80%. Explain what "99% confidence" means in this context.

An educator wanted to look at the study habits of university students. As part of the research, data was collected for three variables - the amount of time (in hours per week) spent studying, the amount of time (in hours per week) spent playing video games and the GPA - for a sample of 20 male university students. As part of the research, a 95% confidence interval for the average GPA of all male university students was calculated to be: (2.95, 3.10). Which of the following statements is true?

An educator wanted to look at the study habits of university students. As part of the research, data was collected for three variables - the amount of time (in hours per week) spent studying, the amount of time (in hours per week) spent playing video games and the GPA - for a sample of 20 male university students. As part of the research, a 95% confidence interval for the average GPA of all male university students was calculated to be: (2.95, 3.10). What assumption is necessary for the confidence interval analysis to work properly?

5% of trucks of a certain model have needed new engines after being driven between 0 and 100 miles. The manufacturer hopes that the redesign of one of the engine's components has solved this problem.

The U.S. Department of Labor and Statistics released the current unemployment rate of 5.3% for the month in the U.S. and claims the unemployment has not changed in the last two months. However, the state's statistics reveal that there is a change in U.S. unemployment rate. What are the null and alternative hypotheses?

Suzie has installed a new spam blocker program on her email. She used to receive an average of 20 spam emails a day. Is the new program working?

An insurance company sets up a statistical test with a null hypothesis that the average time for processing a claim is 7 days, and an alternative hypothesis that the average time for processing a claim is greater than 7 days. After completing the statistical test, it is concluded that the average time exceeds 7 days. However, it is eventually learned that the mean process time is really 7 days. What type of error occurred in the statistical test?

In the past, the mean battery life for a certain type of flashlight battery has been 9.4 hours. The manufacturer has introduced a change in the production method and wants to perform a hypothesis test to determine whether the mean battery life has increased as a result. The hypotheses are:

H₀ : μ = 9.4 hours

H₁ : μ > 9.4 hours

Explain the result of a Type II error.

How many tissues should a package of tissues contain? Researchers have determined that a person uses an average of 40 tissues during a cold. Suppose a random sample of 10,000 people yielded the following data on the number of tissues used during a cold: $$\overline{x}$$ = 31, s = 18. Using the sample information provided, set up the calculation for the test statistic for the relevant hypothesis test, but do not simplify.

A bottling company produces bottles that hold 12 ounces of liquid. Periodically, the company gets complaints that their bottles are not holding enough liquid. To test this claim, the bottling company randomly samples 64 bottles and finds the average amount of liquid held by the bottles is 11.9155 ounces with a standard deviation of 0.40 ounce. Suppose the p-value of this test is 0.0455. State the proper conclusion.