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 7.496 hours. The population standard deviation is 92 hours. A random sample of 64 light bulbs indicatos a sample mean life of 7,473 hours. a. At the 0.05 level of significance, is there evidence that the mean life is different from 7,496 hours? 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 y be the population mean. Determine the null hypothesis, Ho, and the alternative hypothesis, H, HON= H: * What is the best statistic? ZSTAT (Round to two decimal places as needed.) What is/are the critical value(s)? (Round to two decimal places as needed. Use a comma to separate answers as needed.) What is the final conclusion? O A. Fail to reject Ho. There is sufficient evidence to prove that the mean life is different from 7,496 hours. OB. Reject Hp. There is sufficient evidence to prove that the mean life is different from 7.496 hours. O C . Fail to reject Ho. There is not sufficient evidence to prove that the mean life is different from 7.498 hours. OD. Reject Ho. There is not sufficient evidence to prove that the mean life is different from 7,496 hours. b. What is the D-value? Click to select your answer(s)

b. What is the p-value? (Round to three decimal places as needed.) Interpret the meaning of the p-value. Choose the correct answer below. O A. Fail to reject Ho. There is sufficient evidence to prove that the mean life is different from 7,496 hours. OB. Reject Ho. There is not sufficient evidence to prove that the mean life is different from 7,496 hours. O C. Fail to reject Ho. There is not sufficient evidence to prove that the mean life is different from 7,496 hours. OD. Reject Ho. There is sufficient evidence to prove that the mean life is different from 7,496 hours. c. Construct a 95% confidence interval estimate of the population mean life of the light bulbs. sus (Round to one decimal place as needed.) d. Compare the results of (a) and (c). What conclusions do you reach? O A. The results of (a) and (c) are the same: there is sufficient evidence to prove that the mean life is different from 7,496 hours. OB. The results of (a) and (c) are not the same: there is sufficient evidence to prove that the mean life is different from 7,496 hours. O C. The results of (a) and (c) are the same: there is not sufficient evidence to prove that the mean life is different from 7,496 hours.

Answer 1

U VPL Here we have @ M29496, 6 92,,7-7473-*30.05 Hypotheses a Hon4-7496 Hai M7496 test statistic z rest 2 = x 4 7473 - 74 critical value at a=0.05 Zert- 20.05% +131.967 -1.96, 1.96 criitalready critical resion 00025 0.025 here here 1 onco since mat -1.91 0 1.96 z ZSTAT <-1096 we redect to conclusion: correct option B). Redect Ho. There is sufficient evidence to prove that the mean life is different from 7496 heurs. A p value - 2 P12>(-21) Foto =2C1-PL262) -2 (1-0.9773) -10.0456 since qualue <0.05, we resect Hoi correct option @ Redecot How. There is sufficient. evidence to prove that the meon life is different from 7496 hours a A at 95% confidence level a X=1-0.95 -0.05

164 Noor Zerit= 20.05/2 = 1096 are now 95 % cl . De I Zcrit = 7473 I 9.96X92 = 7473 7 22054 ** = 17450.46, 7,495.54_17450.464m s 7495.se since 74.96 does not lie in the above interval . fence we resect Ho . . correct option c o the result of (agle I are the same; there is sufficient evidence to prove that nа mеаи СЕe b6 Үnt [email protected] 74-76 | 07 с.