To test H0: μ = 100 versus H1: μ ≠ 100, a simple random sample of size n = 23 is obtained from a population that is known to be normally distributed.


a. If x̄ = 104.8 and s = 9.2, compute the test statistic.


b. If the researcher decides to test this hypothesis at the α = 0.01 level of significance, determine the critical values.

A simple random sample of size n = 15 is drawn from a population that is normally distributed. The sample variance is found to be 23.8. Determine whether the population variance is less than 25 at the α = 0.01 level of significance.

Quality ControlSuppose the mean wait-time for a telephone reservation agent at a large airline is 43 seconds. A manager with the airline is concerned that business may be lost due to customers having to wait too long for an agent. To address this concern, the manager develops new airline reservation policies that are intended to reduce the amount of time an agent needs to spend with each customer. A random sample of 250 customers results in a sample mean wait-time of 42.3 seconds with a standard deviation of 4.2 seconds. Using an α = 0.05 level of significance, do you believe the new policies were effective? Do you think the results have any practical significance?

Reading Rates The reading speed of second-grade students is approximately normal, with a mean of 90 words per minute (wpm) and a standard deviation of 10 wpm.

e. A teacher instituted a new reading program at school. After 10 weeks in the program, it was found that the mean reading speed of a random sample of 20 second-grade students was 92.8 wpm. What might you conclude based on this result?

Efficacy of e-Cigs Do electronic cigarettes assist in helping individuals quit smoking? Researchers found 300 current smokers to volunteer for a study in which each was randomly assigned to one of three treatment groups. Group 1 received an electronic cigarette (e-cig) in which each cartridge contained 7.2 mg of nicotine, Group 2 received an e-cig that contained 5.4 mg of nicotine, and Group 3 received an e-cig that contained no nicotine. The subjects did not know which group they were assigned. During the course of the 52-week intervention, subjects dropped out of the study. At the end of the study 65 subjects remained in Group 1, 63 in Group 2, and 55 in Group 3. After 52 weeks, it was determined via questionnaire whether the subject quit smoking entirely. Results of the study are presented in the following table.

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e. Does the evidence suggest e-cigs are effective in helping individuals abstain from cigarette smoking? Use the alpha = 0.05 level of significance.

Effects of Alcohol on the BrainIn a study published in the American Journal of Psychiatry (157:737–744, May 2000), researchers wanted to measure the effect of alcohol on the hippocampal region, the portion of the brain responsible for long-term memory storage, in adolescents. The researchers randomly selected 12 adolescents with alcohol use disorders to determine whether the hippocampal volumes in the alcoholic adolescents were less than the normal volume of 9.02 cubic centimeters (cm³). An analysis of the sample data revealed that the hippocampal volume is approximately normal with x̄ = 8.10 cm³ and s = 0.7 cm³. Conduct the appropriate test at the α = 0.01 level of significance.

To test H0: mu = 100 versus Ha: mu > 100, a simple random sample of size n = 35 is obtained from an unknown distribution. The sample mean is 104.3 and the sample standard deviation is 12.4.

b. Use the classical or p-value approach to decide whether to reject the statement in the null hypothesis at the alpha = 0.05 level of significance.

The trade magazine QSR routinely examines fast-food drive-thru service times. Their recent research indicates that the mean time a car spends in a McDonald’s drive-thru is 167.1 seconds. A McDonald's manager in Salt Lake City feels that she has instituted a drive-thru policy that results in lower drive-thru service times. A random sample of 70 cars results in a mean service time of 163.9 seconds, with a standard deviation of 15.3 seconds. Determine whether the policy is effective in reducing drive-thru service times.

c. Conduct the appropriate test to determine if the policy is effective.

TVaholicsAccording to the American Time Use Survey, the typical American spends 154.8 minutes (2.58 hours) per day watching television. A survey of 50 Internet users results in a mean time watching television per day of 128.7 minutes, with a standard deviation of 46.5 minutes. Conduct the appropriate test to determine if Internet users spend less time watching television at the α = 0.05 level of significance.

Source: Norman H. Nie and D. Sunshine Hillygus. “Where Does Internet Time Come From? A Reconnaissance.” IT & Society, 1(2).