Question

for clothing for themselves as compared to 36% of the males. The sample sizes of males and females were not pro they enjoyed shopping for clothing ded. Suppose that of 500 females, 225 said at for themselves while of 300 males, 108 said that they enjoyed shopping for dlothing for themselves. Complete parts (a) through (d) d. What are the answers to (a) through (c) if 114 males enjoyed shopping for clothing for themselves? Is there evidence of a difference between males and females in the proportion who enjoy shopping for alothing for themselves at the 0.01 level of significance? State the null and alternative hypotheses, where 쩌 s the population proportion of females that enjoy shopping for themselves and π 2 is the population proport on of males that enjoy shopping for themselves ZSTAT . □ (Round to two decimal places as needed.) Determine the critical value(s) for this test of hypothesis. The critical value(s) is (are)□ Ty (Round to two decimal places as needed. Use a comma to separate answers as needed) Click to select your answer(s). Fi 9

Answer 1

Option - A) H₀: $\small \pi1 = \pi2$

                  H₁: $\small \pi1 \neq \pi2$

$\small \widehat \pi1$ = 0.45

$\small \widehat \pi2$ = 114/300 = 0.38

The pooled sample proportion( $\small \pi$ ) = ( $\small \widehat \pi1$ * n1 + $\small \widehat \pi2$ * n2)/(n1 + n2 )

                                                      = (0.45 * 500 + 0.38 * 300)/(500 + 300)

                                                      = 0.424

The test statistic z_STAT = ( $\small \widehat \pi1$ - $\small \widehat \pi2$ )/sqrt( $\small \pi$ (1 - $\small \pi$ )(1/n1 + 1/n2))

                                     = (0.45 - 0.38)/sqrt(0.424 * (1 - 0.424) * (1/500 + 1/300)

                                      = 1.94

At apha = 0.01, the critical values are z_0.005 = +/- 2.58

Since the test statistic value is not greater than the upper critical value,(1.94 < 2.58), so we should not reject the null hypothesis.

So there is not sufficient evidence to conclude that there is a difference between males and females in the proportion who enjoy shopping for themselves.