Question

A company is critisized because only 13 of 43 people in executive-level positions are women. The company explains that although the proportion is lower than it might wish, it's not surprising given that only 40% of all their employees are women. What do you think? Test an appropriate hypothesis and state your your conclusion.

Answer 1

Answer:

Given that:

A company is critisized because only 13 of 43 people in executive-level positions are women.The company explains that although the proportion is lower than it might wish, it's not surprising given that only 40% of all their employees are women.

Let us construct a suitable confidence interval and also test this claim with approprite hypothesis

Let p be the proportion of top executive women employees in the company

Let us set up the null hypothesis that H0 the proportion of executive women employees in the company is 0.40 that is p=0.40 against the alternative hypothesis that Ha: the proportion of executive women employees in the company is 0.40.p<0.40

The data regarding the number of women executive cannot be generalized to other companies also

The success and failure condition

The proportion of executive women employees in the company is 0.40

The condition np>10 success is also satisified

That is the number of successes is given by np which is

np=43*0.40=17.2>10

And the number of failures denoted by nq

nq=43*0.60=25.8>10

It is definitely greater than 10 failures and successes

Hence the condition satisfied

The 95% condfidence intervl for p is given by

We can find the confidence interval by using Minitab as follows

In minitab choose stat-basic statistics one sample proportion

Select summarized trails enter the values

Select the test hypothesis set the test vaue click ok to obtain the result as follows

A screen shot of the minitab output is presented below

The p-value of the test is 0.096 from the output.Since the p value is 0.096 is greater than the alpha value of 0.05.We accept the null hypothesis and conclude that the proportion of executive women employees in the company is 40%