Question

1.     In a company, it was observed that the proportion of employees with a Bachelor’s degree is 40%. The board of directors wants to know if the proportion of Bachelor’s degrees earners on the management/executive teams is greater than the proportion company-wide. Test at α = .01 level of significance.

a.     Using the normal approximation for the binomial distribution (without continuity correction), what is the test statistic for this sample proportion? (show work)

                                                       i.          z = _____

                                                     ii.          What is the p-value for this sample? p -value = _______ (report to 4 decimal places)

Answer 1

a - i )  

Formula of z test statistic is as follows

Where = sample proportion

P = given proportion or assume proportion of testing null hypothesis = 0.40

n = sample size

Suppose n = 50 and = 0.56

Then test statistic Z is given by

Note that you need to use given sample size (n) and the given sample proportion in your example to find the Z test statistic .

a - ii)

Here the alternative hypothesis ( H_a ) is as followws:

H_a : P > 0.4

So p-value = P( Z > 2.31 ) = "=1-NORMSDIST(2.31)" = 0.0104

Where "=1-NORMSDIST(2.31)" is the binomial command to find the greater than probability.

Just used your z test statistic value insted of 2.31 in the above command then you get p-value for your example.