At one time, it was reported that 27.9% of physicians are women. In a survey of physicians employed by a large health system, 45 of 120 randomly selected physicians were women. Is there sufficient evidence at the 0.05 level of significance to conclude that the proportion of women physicians in the system exceeds 27.9%?Solve this hypothesis testing problem by finishing the five steps below.

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FineasN267137 FineasN267137 · Answer 1 · 2022-10-25T10:19:35+02:00

SOLUTION

STEP 1

The hull hypothesis can written as

[tex]H_0\colon p=0.279[/tex]

The alternative hypothesis is written as

[tex]H_1\colon p>0.279[/tex]

STEP 2

The value of p will be

[tex]\begin{gathered} \hat{p}=\frac{X}{n} \\ \hat{p}=\frac{45}{120}=0.375 \\ \text{where n=120, x=}45 \end{gathered}[/tex]

STEP3

From the calculations, we have

[tex]\begin{gathered} Z_{\text{cal}}=2.34 \\ \text{Z}_{\text{los}}=0.05 \end{gathered}[/tex]

We obtained the p-value has

[tex]\begin{gathered} p-\text{value}=0.0095 \\ \text{level of significance =0.05} \end{gathered}[/tex]

STEP4

Since the p-value is less than the level of significance, we Reject the null hypothesis

STEP 5

Conclusion: There is no enought evidence to support the claim