1. For each of the following, state the null hypothesis and the alternative hypothesis.
a. The publisher of Celebrity Living claims that the mean sales for personality magazines featuring people such as Angelina Jolie or Paris Hilton is at least 1.5 million per week. A sample of 10 comparable titles shows that the mean weekly sales last week were 1.3 million. The publisher's claim is to be verified.
b. The manager of Little Cakes Inc. states that an average of 1500 muffins is sold each week in the retail store. One of the bakers feels that the average is less than 1500, and decides to test this claim.
c. For the past three years, an insurance company has stated that its average claim amount is $2000. The manager feels that this amount should be updated and takes a sample of 55 claims to see if there is a difference in the average claim amount.
d. A machine on a production line is set to automatically fill each bottle with 500 mL of water. The quality control manager regularly takes random samples of the bottles from the production line to ensure that the machine is filling the bottles correctly, If not, the machine will need adjusting.
2. The following information is available.
H0: μ ≤ 10
H1: μ > 10
The sample mean is 12 for the sample of 36. The population standard deviation is 3. Use the .02 significance level.
a. Is this a one- or two-tailed test?
b. What is the decision rule?
c. What is the value of the test statistic?
d. What is your decision regarding H0?
e. What is the p-value? Interpret it.
3. The MacBurger restaurant chain claims that the waiting time of customers for service is normally distributed, with a mean of 3 minutes and a standard deviation of 1 minute. The quality control department found in a sample of 50 customers at the Warren Road MacBurger that the mean waiting time was 2.75 minutes. Can we conclude that the mean waiting time is less than 3 minutes?
Use α = .05.
a. State the null hypothesis and the alternative hypothesis.
b. State the decision rule.
c. Compute the value of the test statistic.
d. What is your decision regarding H0?
e. What is the p-value? Interpret it.
4. Given the following hypotheses:
H0: μ = 400
H1: μ ≠ 400
For a random sample of 12 observations, the sample mean was 407 and the sample standard deviation 6. Using the .01 significance rule.
a. State the decision rule.
b. Compute the value of the test statistic.
c. What is your decision regarding the null hypothesis?
5. The liquid chlorine added to swimming pools to combat algae has a relatively short shelf life before it loses its effectiveness. Records indicate that the mean shelf life is 4.5 L jug of chlorine is 2160 hours (90 days). As an experiment, Holdlonger was added to the chlorine to find whether is would increase the shelf life. A sample of nine jugs of chlorine had these shelf lives (in hours):
2159 2170 2180 2179 2160 2167 2171 2181 2185
At the .025 level, has Holdlonger increased the shelf life of the chlorine? Determine or estimate the p-value.
6. The following hypotheses are given.
H0: p = .40
H1: p ≠ .40
A sample of 120 observations revealed that p' = .30. At the .05 significance level, can the null hypothesis be rejected?
a. State the decision rule.
b. Compute the value of the test statistic.
c. What is your decision regarding the null hypothesis?
Note: It is recommended that you use the five-step hypothesis procedure in solving the following problems.
7. Research at a university indicates that 5 percent of the students change their major area of study after their first year in a program. A random sample of 100 students in business revealed that 48 had changed their major area of study after their first year of the program. Has there been a significant decrease in the proportion of students who change their major after the first year in this program? Choose an appropriate level of significance.