Question

A large retailer observes the percentage of customers who leave its stores with a purchase. It would like to investigate if the percentage of women who leave the store with a purchase is lower than the percentage of men. In a randcm sample of 170 female shoppers, 149 left the store with a purchase. In a random sample of 140 male shoppers, 135 left the store with a purchase. Complete parts a and b below a. Perform a hypothesis test with α=0.10 to determine if the percentage of women who leave the store with a purchase is lower than the percentage of men. Let population 1 be women and population 2 be men. What are the correct null and alternative hypotheses? HがP1-P2:0 Ho : p1-p2 z 0 H1:P1-P20 H1 : p1-p2 #0 D. Ho: P1-P2>0 C. What is the test slatistic? pRound to two decimal places as needed.) What is/are the critical value(s)? The critical value(s) is/are Round to two decimal places as needed. Use a comma to separate answers as needed.) Interpret the results. Choose the correct answer below. O A. Do not reject Hp. There is sufficient evidence to support the claim that the percentage of women who leave the store with a purchase is lower than the percentage of men. 。B. Do not reject There is not sufficient evidence o support the claim that the percentage o women who leave the stre with a purchase is lower than the percentage of men. C. Reject H0. There is sufficient evidence to support the claim that the percentage of women who leave the store with a purchase is lower than the percentage of men. Reject Ho. There is not sufficient evidence to support the claim that the percentage of women who leave the store with a purchase is lower than the percentage of men. D.b. Determine the p-value and interpret the results. alue(Round to three decimal places as needed.) Interpret the results. Choose the correct answer below. ○ A. Do not reject Ho . There is sufficient evidence to support the claim that the percentage of women who leave the store with a purchase is lower than the percentage of men. O B Do not relect o There is not sufficient evidence to support the claim that the percentage of women who leave the store with a purchase is lower than the percentage of en O C. Reject Ho. There is not sufficient evidence to support the claim that the percentage of women who leave the store with a purchase is lower than the percentage of men 。D. Reject Ho There is sufficient evidence to support the claim that the percentage of women who leave the store with a purchase is lower than the percentage of men.

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Answer #1

For sample 1, we have that the sample size is N1-. 170, the number of favorable cases is х, , so then the sample proportion is p,-4 = 0.8765 For sample 2, we have that the sample size is N2 140, the number of favorable cases is X2 , so then the sample proportion is p2-X2-140-09643 The value of the pooled proportion is computed as p- N2-TAM-09161 Also, the given significance level is a 0.1 149 135 X2-135 149+135 170+1 The following null and alternative hypotheses need to be tested This corresponds to a left-tailed test, for which a z-test for two population proportions needs to be conducted (2) Rejection Region Based on the information provided, the significance level is a 0.1, and the critical value for a left- tailed test is ic =-1.28 The rejection region for this left-tailed test is R = {:芯<一1.28) The z-statistic is computed as follows Pi P2 0.8765 0.9643 VP(1 (1/ni +1/n2) V0.9161 (1-0.9161) (1/170 +1/140) Since it is observed rejected Using the P-value approach: The p-value is p = 0.0028, and since p 0.0028 < 0.1, it is concluded that the null hypothesis is rejected (5) Conclusion It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that population proportion pi is less than p2, at the 0.1 significance level ~ =-2.776 < ~c- 1.28, it is then concluded that the nul, hypothesis is

a)
option C)

Zp= -2.776
critical value = -1.28

interpret the results
option C)

b)
p-value = 0.0028
=0.003

option D)

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