Exam 8: Large-Sample Estimation

Lifetime of Laptop Batteries Narrative The manufacturer of a particular battery pack for a laptop computer claims the battery pack can function for 8 hours, on average, before having to be recharged. A random sample of 36 such battery packs was selected and tested. The mean and standard deviation were found to be 6 hours and 1.8 hours, respectively. -Refer to Lifetime of Laptop Batteries Narrative. Find a 90% confidence interval for the true average time the battery pack can function before having to be recharged.

Defective Glass Bottles Narrative A manufacturing plant has two assembly lines for producing glass bottles. The plant manager was concerned about whether the proportion of defective bottles differs between the two lines. Two independent random samples were selected and the following summary data computed: -Refer to Defective Glass Bottles Narrative. Based on the interval in the previous question, can one conclude there is a difference in proportion of defective bottles produced by the two lines? Justify your answer.

The term confidence level refers to an estimate of a population parameter, expressed as a range of values within which the unknown but true parameter presumably lies.

A confidence interval for the population proportion p may or may not contain the true value of p.

Suppose a 95% confidence interval for the mean height of a 12-year-old male in Canada is 137 to 165 cm. It can be said that 95% of 12-year-old males in Canada have height greater than or equal to 137 cm and less than or equal to 165 cm.

In developing an interval estimate for the population mean , the population standard deviation was assumed to be 6. The interval estimate was 45.0 1.5. Had equalled 12, the interval estimate would be 90 3.

Online Time Usage Narrative An Internet server conducted a survey of 400 of its customers and found that the average amount of time spent online was 12.5 hours per week, with a standard deviation of 5.4 hours. -Refer to Online Time Usage Narrative. Do you think that the random variable x, the number of hours spent online, has a mound-shaped distribution? If not, what shape do you expect?