Question

The? quality-control manager at a compact fluorescent light bulb? (CFL) factory needs to determine whether the mean life of a large shipment of CFLs is equal to 7 comma 462 hours. The population standard deviation is 92 hours. A random sample of 64 light bulbs indicates a sample mean life of 7 comma 439 hours. a. At the 0.05 level of? significance, is there evidence that the mean life is different from 7 comma 462 hours question mark b. Compute the? p-value and interpret its meaning. c. Construct a 95?% confidence interval estimate of the population mean life of the light bulbs. d. Compare the results of? (a) and? (c). What conclusions do you? reach? a. Let mu be the population mean. Determine the null? hypothesis, Upper H 0?, and the alternative? hypothesis, Upper H 1. Upper H 0?: muequals nothing Upper H 1?: munot equals nothing What is the test? statistic? Upper Z Subscript STATequals nothing ?(Round to two decimal places as? needed.) What? is/are the critical? value(s)? nothing ?(Round to two decimal places as needed. Use a comma to separate answers as? needed.) What is the final? conclusion? A. Fail to reject Upper H 0. There is not sufficient evidence to prove that the mean life is different from 7 comma 462 hours. B. Fail to reject Upper H 0. There is sufficient evidence to prove that the mean life is different from 7 comma 462 hours. C. Reject Upper H 0. There is not sufficient evidence to prove that the mean life is different from 7 comma 462 hours. D. Reject Upper H 0. There is sufficient evidence to prove that the mean life is different from 7 comma 462 hours. b. What is the? p-value? nothing ?(Round to three decimal places as? needed.) Interpret the meaning of the? p-value. Choose the correct answer below. A. Fail to reject Upper H 0. There is not sufficient evidence to prove that the mean life is different from 7 comma 462 hours. B. Reject Upper H 0. There is not sufficient evidence to prove that the mean life is different from 7 comma 462 hours. C. Reject Upper H 0. There is sufficient evidence to prove that the mean life is different from 7 comma 462 hours. D. Fail to reject Upper H 0. There is sufficient evidence to prove that the mean life is different from 7 comma 462 hours. c. Construct a? 95% confidence interval estimate of the population mean life of the light bulbs. nothingless than or equalsmuless than or equals nothing ?(Round to one decimal place as? needed.) d. Compare the results of? (a) and? (c). What conclusions do you? reach? A. The results of? (a) and? (c) are not the? same: there is not sufficient evidence to prove that the mean life is different from 7 comma 462 hours. B. The results of? (a) and? (c) are the? same: there is sufficient evidence to prove that the mean life is different from 7 comma 462 hours. C. The results of? (a) and? (c) are not the? same: there is sufficient evidence to prove that the mean life is different from 7 comma 462 hours. D. The results of? (a) and? (c) are the? same: there is not sufficient evidence to prove that the mean life is different from 7 comma 462 hours.

Answer 1

a) H0: The mean life is not different from 7462 hours
i.e. H0: Mu = 7462
H1: The mean life is different from 7462 hours
i.e. H1: Mu not = 7462
Let the los be alpha = 5%

Test statstic
Z = (7439 - 7462) / (92/sqrt(64)) = -2

b) P-Value: 0.0455

Here P-value is less then alpha 0.05 so we reject H0
Thus we conclude that the mean life is different from 7462 hours

i.e. There is sufficient evidence to prove that the mean life is different from 7462 hours.

c) The 95% confidence interval of population Mean is
7439 +/- 1.96 * 92 / sqrt(64) = 7439 +/- 22.54 = (7416.46,7461.54)