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 8 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.
(b)	Construct a 95% confidence interval for the porportion of returns at the Houston store. If required, round your answer to three decimal places.
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(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.
	We - Select your answer -reject or fail to reject Item 4 the null hypothesis. We - Select your answer -can or cannot Item 5 conclude that the return rate for the Houston store is different than the U.S. national return rate.

Please explain using excel formulas

Answer 1

Date: 11/11/2019 Answer а) The point estimate of the proportion of items returned for the population of sales transactions at the Houston store is, х р 8 80 0.100 The point estimate of the proportion of items returned for the population of sales transactions at the Houston store is 0.100 b) A 95% confidence interval for the proportion of returns at the Houston store is, First, compute the z-critical value then find confidence interval

The z-critical value is, From the standard normal table, the z-critical value at 95% confidence is 1.96 |P(1- p) 95% C.I. ptZc X. 0.100(1-0.100) =0.100 t1.96x 80 0.034 to 0.166 A 95% confidence interval for the proportion of returns at the Houston store is 0.034 to 0.166 c) To test the hypothesis is that the population proportion return rate for the Houston store is different from 6% at 5% level of significance.

The null and alternative hypothesis is, Ho p 0.06 Hap 0.06 The z-test statistics is, р-р [Р1-р) 8/80 0.06 0.06(1-0.06) 80 - 1.51 The z-test statistics is 1.51. The z-critical value is,

From the standard normal table, the z-critical value for two-tailed at 95% confidence is 1.96 The z-criticalvalue is-1.96 and 1.96 Decision The z-test statistics which is 1.51 corresponds to sample statistics is not falls in the critical region which is 1.96, so fail to reject the null hypothesis at 5% significance level It cannot conclude that the population proportion return rate for the Houston store is different from 6%. The result is not statistically significant.