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 7 of the items were returned.

(a)	Construct a point estimate of the proportion of items returned for the population of sales transactions at the Houston store. If required, round your answer to three decimal places.
(b)	Construct a 95% confidence interval for the proportion 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.

Answer 1

a) n = 80, x = 7

Point estimate = x/n = 7/80 = 0.088

b) 95% Confidence interval :            

At α = 0.05, two tailed critical value, z crit = NORM.S.INV(0.05 / 2) = 1.96
                  
Lower Bound = p̄ - z-crit*(√( p̄ *(1- p̄ )/n)) = 0.026   
                  
Upper Bound = p̄ + z-crit*(√( p̄ *(1- p̄ )/n)) = 0.150

c) Population proportion = 0.06

Since the interval includes 0.06, the proportion of returns at the Houston store is not significantly different from the returns for the nation as a whole.