# Math’s statistics

DSC 670 Assignment 8

1. “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. Assume from past information that it is known that the standard deviation of the population is 9 hours.
 a. Use a 0.01 level of significance, and test to determine if there has been an increase in the life expectancy of the “D” size batteries. b. What is the p-value associated with the sample results? What is your conclusion, based on the p-value?

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1. In order to determine the average price of hotel rooms in Atlanta, a sample of 64 hotels was selected. It was determined that the average price of the rooms in the sample was \$112. The population standard deviation is known to be \$16. Use a 0.05 level of significance and determine whether or not the average room price is significantly different from \$108.50.

1. Bastien, Inc. has been manufacturing small automobiles that have averaged 50 miles per gallon of gasoline in highway driving. The company has developed a more efficient engine for its small cars and now advertises that its new small cars average more than 50 miles per gallon in highway driving. An independent testing service road-tested 36 of the automobiles. The sample showed an average of 51.5 miles per gallon. The population standard deviation is 6 miles per gallon.
 a. With a 0.05 level of significance, test to determine whether or not the manufacturer’s advertising campaign is legitimate. b. What is the p-value associated with the sample results?

1. A carpet company advertises that it will deliver your carpet within 15 days of purchase. A sample of 49 past customers is taken. The average delivery time in the sample was 16.2 days. The population standard deviation is 5.6 days.
 a. State the null and alternative hypotheses. b. Using a critical value, test the null hypothesis at the 5% level of significance. c. Using a p-value, test the hypothesis at the 5% level of significance. d. Compute the probability of a Type II error if the true average delivery time is 17 days after purchase.

1. For each shipment of parts a manufacturer wants to accept only those shipments with at most 10% defective parts. A large shipment has just arrived. A quality control manager randomly selects 50 of the parts from the shipment and finds that 6 parts are defective. Is this sufficient evidence to reject the entire shipment? Use a .05 level of significance to conduct the appropriate hypothesis test.

1. A national poll reported that 58% of those with Internet access have made purchases online. To investigate whether this percentage applies to its own state, a legislator commissions a study. A random sample of 400 state residents who have Internet access is taken. Of those 400 respondents, 215 said that they have made purchases online. Does this sample provide sufficient evidence to conclude that the state differs from the nation with respect to making purchases online? Use the p-value to conduct the hypothesis test and use a .05 level of significance.

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