Question

According to the University of Nevada Center for Logistics Management, 6% of all merchandise sold in the United States gets returned. A Houston department store sampled 80 items sold in January and found that 11 of the items were returned

According to the University of Nevada Center for Logistics Management, 6% of all merchandise sold in the United States gets returned. A Houston department store sampled 80 items sold in January and found that 11 of the items were returned. (a) Construct a point estimate of the proportion of items returned for the population ofsales transactions at the Houston store. If required, round your answer to three decimal places. 1375 (b) Construct a 95% confidence interval for the porportion of returns at the Houston store. If required, round your answer to three decimal places. to (C) Is the proportion of returns at the Houston store significantly different from the returns for the nation as a whole? Provide statistical support for your answer. W - Select your answer - the null hypothesis. We - Select your answer - conclude that the return rate for the Houston store is different than the U.S. national return reject fail to reject

A shareholders' group, in lodging a protest, claimed that the mean tenure for a chief executive officer (CEO) was at least nine years. A survey of companies reported in The Wall Street Journal found a sample mean tenure of x = 7.67 years for CEOs with a standard deviation of s = 6.38 years.

Answer 1

1. Let p denotes the true proportion of returns at the Houston store.

b)

Let p denotes the sample proportion and n denotes the sample size Here, 0.1375 (1 0.1375) p 0.1375, n = 80, standard error = 0.038502 80 Margin of error is *(1 -p) 0.137500 (1 - 0.137500) 0.137500 (1- 0.137500) 1.644854 0.063331 0.0633 МЕ 20.025 21-0.95 80 80 n 2 a 95 percent confidence interval for the population proportion p is p*(1-p) 21-0.95 n 2 0.1375 (1 0.1375) = 0.138 t 20.025 80 0.1375 (1 0.1375) = 0.138 t 1.959964 80 = 0.138 t 0.063331 = (0.074169, 0.200831) (0.074,0.201)

We reject the null hypothesis. We can conclude that the return rate for the Houston store is different than the U.S. national return rate.

2.

To test null hypothesis Ho 9.00 against alternative hypothesis H1 9.00 Let denotes the sample mean, s denotes the sample standard deviation and n denotes the sample size. Here, 7.6700, s = 40.7044, s = 6.3800, n 85 The test statistic can be written as п (+ — 9.00) t = S which under Ho follows a t distribution with n-1 df. We reject Ho at 0.01 level of significance if P-value < 0.01 or if tobs < -to.010,n-1 Now, The value of the test statistic -1.921943 associated degrees of freedom = 84 The critical value -2.371564 P - value P(t84 < tobs)= P(ts4<-1.921943) 0.029002 0.0290 Since p-value > 0.01 and tobstcritical = -2.371564, so we fail to reject Ho at 0.01 level of significance Hence, we can conclude that population mean is not significantly less than 9.00

b) P-value = 0.0290

c) We fail to reject the null hypothesis. We can not conclude that the mean tenure for a CEO is shorter than nine years.