A company is criticized because only 15 of 44 people in executive-level position

Question

A company is criticized because only 15 of 44 people in executive-level positions are women. The company explains that although this proportion is lower than it might wish, irs not surprising given that only 41% of their employees are men. The company has more than 500 executives word ido W hat do you think? Test an appropriate hypothesis with =05 and state your coolusion. Be sure the appropriate assumptons and condi itions are satisfied before you proceed. HA:p>0.41 Ho: P 0.41 HA p041 Calculate the test statistic. HA:p#0.41 H0: p#0.41 HA: p= 041 OF, OA(Round to two decimal places as noeded ) O B. The test statistic cannot be calculated. The conditions for a hypothesis test are not all met

Explanation / Answer

n =total number of people in executive level positions =44

x =number of people in executive level positions are women =15

p =propertion of people in executive level position are women = 15/44 = 0.3409

Here We want to test the hypotjesis that propertion of people in executivel level positions are women less than 0.41

i.e We want to test the hypothesis that

Ho: p = 0. 41 against HA : p < 0.41 (left-tailed test)

Under Ho the test statistic is

z = (p-p0 ) / sqrt (p0 *q0 /n) ~ N(0,1) where q0 = 1-p0

z = ( 0.3409 - 0.41 ) / sqrt ( 0.41 *0.59 /44)

z = -0.0691 / 0.0741= -0.8343

z = -0.8343

Table value

alpha : level of significance = 0.05

z alpha = Z 0.05 = 1.64

Since test is left -tailed test and z = -0.8343 > -1.64 hence test is not significant. We accept Ho at 5% level of significance.

Conclusion : propertion of people in executivel level positions are women are 0.41.

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