Question

Part B. Calculate the Z stat

PartC. Calculate the P value

9.4.57-1 Recently a large academic medical center determined that 15 of 24 employees a pat cular ost were male w e as % o the employ tb-poste ni e t- o meere male. At the 0 05 level of significance, is there eidenice that the proportion of males in this postion at this medical center is different fom what would be expected in the general workcforce? What are the correct hypotheses to test to determine if the proportión is dferent?

Answer 1

A) Option - B) H₀: $\pi$ = 0.42

                   H₁: $\pi \neq$ 0.42

B) $\widehat \pi$ = 15/24 = 0.625

The test statistic z = ( $\widehat \pi$ - $\pi$ )/sqrt( $\pi$ (1 - $\pi$ )/n)

                             = (0.625 - 0.42)/sqrt(0.42 * (1 - 0.42)/24)

                             = 2.03

C) P-value = 2 * P(Z > 2.03)

                  = 2 * (1 - P(Z < 2.03))

                  = 2 * (1 - 0.9788)

                  = 2 * 0.0212

                  = 0.0424

As the P-value is less than the signifiance level (0.0424 < 0.05), we should reject the null hypothesis.

At 0.05 significance level, there is sufficient evidence to support the claim that the proportion of males in this position at this medical center is different from what would be expected in the general workforce.