# Statistics Ten Multiple Problems

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For problems 1 – 3 you are to use the p-value approach to test the hypotheses where σ is known.

1.A university advises parents of incoming freshmen that the average cost of textbooks is typically greater than \$300. A sample of 35 students enrolled in the university indicates a sample mean cost of \$295.40. Assume the population standard deviation is \$23.20. With a 0.05 level of significance, use the p-value approach to test the university’s claim that the average cost of textbooks is greater than \$300.

HO: μ "State the null hypothesis."
HA: μ "State the alternativel hypothesis."
"State the rejection rule"

"Compute the test statistic for the test stated in the problem"
"State if you reject or fail to reject the null hypothesis."

2.You are a manager of a fast food restaurant. The population mean waiting time to place an order is 4.5 minutes with a population standard deviation of 1.4 minutes. You want to test if the waiting time to place an order has changed from the 4.5 minutes. You select a sample of 49 orders during a one hour period. The sample mean is 5.0 minutes. Use a 0.05 level of significance, and the p-value approach to test if there has been a change in the mean waiting time to place an order.

HO: μ "State the null hypothesis."
HA: μ "State the alternativel hypothesis."
"State the rejection rule"
"Compute the test statistic for the test stated in the problem"
"State if you reject or fail to reject the null hypothesis."

3."D" size batteries produced by MNM Corporation have had a life expectancy of 87 hours. Because of an improved production process, the company believes that there has been an increase in the life expectancy of its "D" size batteries. A sample of 36 batteries showed an average life of 88.5 hours. The standard deviation of the population is 9 hours. Use a 0.01 level of significance and the p-value approach to test if there has been an increase in the life expectancy of the "D" size batteries.

HO: μ "State the null hypothesis."
HA: μ "State the alternativel hypothesis."
"State the rejection rule"
"Compute the test statistic for the test stated in the problem"
"State if you reject or fail to reject the null hypothesis."

For problems 4 – 6 you are to use the critical-value approach to test the hypotheses where σ is known.

4.A lathe is set to cut bars of steel into lengths of 6 centimeters. The lathe is considered to be in perfect adjustment if the average length of the bars it cuts is 6 centimeters. If the bars are cut at any other length the lathe will have to be adjusted. A sample of 121 bars is selected randomly and measured. It is determined that the average length of the bars in the sample is 6.08 centimeters. The population standard deviation is 0.44 centimeters. Use the critical value approach to determine whether or not the lathe is in perfect adjustment. Use a .05 level of significance.

HO: μ "State the null hypothesis."
HA: μ "State the alternativel hypothesis."
"State the rejection rule"
"Compute the test statistic for the test stated in the problem"
"State if you reject or fail to reject the null hypothesis."

5.A carpet company advertises that it will deliver your carpet within 15 days of purchase. The company wants to check and see if its deliveries are being made within 15 days of purchase as promised. A sample of 49 past customers is taken. The average delivery time in the sample was 16.2 days. Assume the population standard deviation is known to be 5.6 days. Use the critical value approach to test the null hypothesis at a level of significance of .01.

HO: μ "State the null hypothesis."
HA: μ "State the alternativel hypothesis."
"State the rejection rule"
"Compute the test statistic for the test stated in the problem"
"State if you reject or fail to reject the null hypothesis."

6. The makers of an exercise machine claim that using their machine for only 6 minutes a day results in an average weight loss of 8 pounds or more during the first week. A consumer group recruited 40 volunteers to use the machine according to the manufacturer’s recommendations and found an average weight loss of 6.7 pounds. Assume the population standard deviation is 3.1 pounds. Use the critical value approach to test the manufacturer’s claim at the .01 level of significance.

HO: μ "State the null hypothesis."
HA: μ "State the alternativel hypothesis."
"State the rejection rule"
"Compute the test statistic for the test stated in the problem"
"State if you reject or fail to reject the null hypothesis."

For problems 7 – 8 you are to use the p-value approach to test the hypotheses where σ is not known.

7. A local brewery wishes to ensure that an average of 12 ounces of beer is used to fill each bottle. In order to analyze the accuracy of the bottling process, the bottler takes a random sample of 25 bottles. The sample mean weight was 11.8 ounces and the sample standard deviation was 0.6 ounces. Adjustments to the bottling process are necessary if more or less than 12 ounces is being dispensed. Use the p-value approach to test if the bottling process needs adjustment. Use a .05 level of significance.

HO: μ "State the null hypothesis."
HA: μ "State the alternativel hypothesis."
"State the rejection rule"
"Compute the test statistic for the test stated in the problem"
"State if you reject or fail to reject the null hypothesis."

8. Figures released by the U.S. Department of Agriculture showed that in 1997 the average size of a farm was 471 acres. An agribusiness researcher believes the average size of farms has now increased from the 1997 figure of 471 acres. To test this, a random sample of 23 farms was surveyed. This sample produced a sample mean of 498 acres with a sample standard deviation of 47 acres. Use the p-value approach to test the researcher’s claim at a .05 level of significance.

HO: μ "State the null hypothesis."
HA: μ "State the alternativel hypothesis."
"State the rejection rule"
"Compute the test statistic for the test stated in the problem"
"State if you reject or fail to reject the null hypothesis."

For problems 9 – 10 you are to use the critical-value approach to test the hypotheses where σ is not known.

9.A cookie company claims that each of their chocolate chip cookies has at least 9 chocolate chips. A sample of 16 cookies is taken to test the claim that each cookie contains at least 9 chocolate chips. The mean number of chocolate chips per cookie in the sample was 7.875 with a sample standard deviation of 1.6 chips. Use the critical value approach to test the hypothesis at the .01 level of significance.

HO: μ "State the null hypothesis."
HA: μ "State the alternativel hypothesis."
"State the rejection rule"
"Compute the test statistic for the test stated in the problem"
"State if you reject or fail to reject the null hypothesis."

10.The EPA recommends that farm-raised salmon contain no more than 0.08 ppm of the insecticide Mirex. A food inspector took a sample of 18 fish and found the mean amount of Mirex to be .084 ppm with a sample standard deviation of .011 ppm . Use the critical value approach to test whether the farm-raised salmon meet the EPA’s recommendation at the .05 level of significance.

HO: μ "State the null hypothesis."
HA: μ "State the alternativel hypothesis."
"State the rejection rule"
"Compute the test statistic for the test stated in the problem"
"State if you reject or fail to reject the null hypothesis."

• 7 years ago
Statistics Ten Multiple Problems with Detailed Solution
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