Question

A company is criticized because only 15 of 41 people in​ executive-level positions are women. The company explains that although this proportion is lower than it might​ wish, it's not surprising given that only 44​% of their employees are women. The company has more than 500 executives worldwide. What do you​ think? Test an appropriate hypothesis with alpha equals 0.05 and state your conclusion. Be sure the appropriate assumptions and conditions are satisfied before you proceed. Determine the hypotheses for this test.​ (The proportion of female executives in the entire company is denoted by​ p.) A. Upper H 0​: pless than or equals0.44 Upper H Subscript Upper A​: pequals0.44 B. Upper H 0​: pequals0.44 Upper H Subscript Upper A​: pnot equals0.44 C. Upper H 0​: pnot equals0.44 Upper H Subscript Upper A​: pequals0.44 D. Upper H 0​: pequals0.44 Upper H Subscript Upper A​: pgreater than0.44 E. Upper H 0​: pequals0.44 Upper H Subscript Upper A​: pless than0.44 F. Upper H 0​: pgreater than or equals0.44 Upper H Subscript Upper A​: pequals0.44 Calculate the test statistic. A. zequals nothing ​(Round to two decimal places as​ needed.) B. The test statistic cannot be calculated. The conditions for a hypothesis test are not all met. Find the​ P-value. A. ​P-valueequals nothing ​(Round to three decimal places as​ needed.) B. The​ P-value cannot be calculated. The conditions for a hypothesis test are not all met. State the conclusion of the test. Choose the correct answer below. A. Because the​ P-value is​ high, reject Upper H 0. These data do not show that the proportion of women executives in the company is less than the 44​% of women in the company in general. B. Because the​ P-value is​ high, fail to reject Upper H 0. These data do not show that the proportion of women executives in the company is less than the 44​% of women in the company in general. C. Because the​ P-value is​ low, fail to reject Upper H 0. These data show that the proportion of women executives in the company is less than the 44​% of women in the company in general. D. Because the​ P-value is​ low, reject Upper H 0. These data show that the proportion of women executives in the company is less than the 44​% of women in the company in general.

Answer 1

From the given information,

1. Hypothesis

H 0​: p=0.44 HA​: p<0.44

i.e., Option E. is correct.

2. A) Test statistic,

z= -0.96

3. P-value= 0.169

4. Because the​ P-value is​ high, fail to reject Upper H 0. These data do not show that the proportion of women executives in the company is less than the 44​% of women in the company in general.

Hence, Option B. is correct.

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