Question

You may need to use the appropriate appendix table or technology to answer this question. CCN and ActMedia provided a television channel targeted to individuals waiting in supermarket checkout lines. The channel showed news, short features, and advertisements. The length of the program was based on the assumption that the population mean time a shopper stands in a supermarket checkout line is 8 minutes. A sample of actual waiting times will be used to test this assumption and determine whether actual mean waiting time differs from this standard. (a) Formulate the hypotheses for this application. o House Hu> 8 Hou > 8 H: 458 Hou = 8 Hau + 8 Hoiu <8 Hai u 8 O Hou 28 Hau<8 (b) A sample of 105 shoppers showed a sample mean waiting time of 8.4 minutes. Assume a population standard deviation of o = 3.2 minutes. What is the test statistic? (Round your answer to two decimal places.) What is the p-value? (Round your answer to four decimal places.) p-value = (c) At a = 0.05, what is your conclusion? Reject Ho. There is insufficient evidence to conclude that the population mean waiting time differs from 8 minutes. Reject Ho. There is sufficient evidence to conclude that the population mean waiting time differs from 8 minutes. Do not reject Ho. There is sufficient evidence to conclude that the population mean waiting time differs from 8 minutes. O Do not reject Ho. There is insufficient evidence to conclude that the population mean waiting time differs from 8 minutes. (d) Compute a 95% confidence interval for the population mean. (Round your answers to two decimal places.) to Does it support your conclusion? The confidence interval --Select--- the hypothesized value of Mor therefore we --Select--- VH. The conclusion -Select-- the same as in part (c).

Answer 1

test against To Ha: u #8 time. mean u es Solution : Ho: u=8 where the population The hypotheses as are a Hoo u (a) Hai e & 9 105, 16 3-2 minules, lo & mins & n = 8.4mins, o

Limit Theorem, central As n es large, using affroad in the say sample can we x is that arX mean. w (wo), where 7 As the population standard deviation the test known is statistie given by Sn(G-.0) Z INNLOD under Ho. 5105 (0.4-8) Z The oralue cig 3.21 tragsta 1:28 de int Now , 0.100 3. 0.2005 2 X 0.1003 0:05, then Plz 31-23) = 1- P(Z 5.1-23) p-value (E) If Do not reject Ho. There is insufficient evidence to conclude that the population time differs from 8 minutes. 2 0:2005 paralue 0.05 mean waiting

interval for the for the population A (a) 95% confidence is ginen by, mean Chere). ot 0.05 ti a Z olis 2시2 Zoo 25 21.96 o = 3.22 ns105, 8.4. Here The CI is 957 7.79 , quoi . arth 954 tion mean is confidence, the populati betrecer 7.79 and 9.01 minules. Internal contains mean allo, the population hypothesized value Level siamieance 54. not reject Ho. Since the congidence the of at 4ܝ we do