Question

According to the University of Nevada Center for Logistics Management, 11% of all merchandise sold in the United States gets returned. A Houston department store sampled 100 fers 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 of sales transactions at the Houston store (to 1 decimals) b. Construct a 95% confidence interval for the proportion of returns at the Houston store (to 4 decimals) Is the proportion of returns at the Houston store significantly different from the returns for the nation as a whole provide statistical H H p Select your answer 0.11 P Select your answer 0.11 ve (to 2 decimal) p-value o decimos Select your answer the null. Yes, weselect your answer enough evidence to prove that Houston is different from the national average

Answer 1

a) Point estimate of the proportions of items returned :    $\hat{p} = \frac{11}{100} = 0.11$

b) Standard error

$SE= \sqrt{\frac{\hat{p} (1-\hat{p} )}{n}} = \sqrt{ \frac{0.11(1-0.11)}{100}}$

Margin of error : $ME= z_{1-\alpha /2} \times \sqrt{\frac{\hat{p} (1-\hat{p} )}{n}} = 1.96\times \sqrt{ \frac{0.11(1-0.11)}{100}} =0.0613$

So, 95%confidence interval is :   

$\hat{p} \pm ME \\ =( 0.11 \pm 0.0613) \\ =(0.0487 , 0.1713)$

c)    $H_0: p_0 = 0.11 \ \ H_1 : p_0 \ne 0.11$

  

z value / Test statistics :

$z = \frac{\hat{p}- p }{\sqrt{\frac{\hat{p} (1-\hat{p} )}{n}}} = 0$ as $\hat{p} = p =0.11$

z value / critical value = 1.96

p value = 1

Fail to reject the null , yes we don't have enough evidence to prove that Huston is different from the national average.