Question

Last year, 50% of MNM, Inc., employees were female. It is suspected that there has been a reduction in the percentage of females in the company. This year, in a random sample, 400 employees were male, 380 were female.

a. State the null and the alternative hypotheses.

b. At the .05 level using the critical value approach, determine if there has been a significant reduction in the proportion of females.

c. Show that the p-value approach results in the same conclusion as that of part b

Answer 1

Answer:

Given that,

Last year, 50% of MNM, Inc., employees were female. It is suspected that there has been a reduction in the percentage of females in the company.

This year, in a random sample, 400 employees were male, 380 were female.

Let p be the proportion of the employee is female.

Given that last year, female employees are 50%.

(a).

State the null and the alternative hypotheses:

Test Hypotheses are:

The null hypothesis:

The alternative hypothesis:

(Left tail test)

Level of significance =0.05.

(b).

At the .05 level using the critical value approach.

Determine if there has been a significant reduction in the proportion of females:

The test statistic is,

Where,

The sample proportion () =x/n

=380/400

=0.95

P= Population proportion=0.5

Q=1-P

=1-0.5

=0.5

Sample size (n)=400

Then,

=0.45/0.025

Z=18

Criterion: Zc at 0.05 level of significance is 1.645.

If Z > Zc.

We fail to reject H0.

Conclusion:

Z=18 > -1.645=Zc

Hence we fail to reject the null hypothesis.

(c).

Show that the p-value approach results in the same conclusion as that of part b:

The p-value at Z=18 and =0.05 is,

The P-Value is < 0.00001.

(From the z-score table)

The result is significant at p < 0.05.

Since the p-value very less than that of the level of significance 0.05.

H0 is rejected.

Therefore, part b and part c answers are different.

** Please comment on any doubts.