Question

A company is criticized because only 20 of 47 executives at a local branch are women. The company explains that although this proportion is lower than it might​ wish, it's not a surprising value given that only 45​% of all its employees are women. The company has more than 500 executives worldwide. Test an appropriate hypothesis and state the conclusion.

Answer 1

Answer:

There is insufficient evidence to support the claim that  it's not a surprising value given that only 45​% of all its employees are women

Step-by-step explanation:

-Given that $p_o=0.45, n=47, x=20$

-We state our hypothesis as:

$H_o:p=0.45\\\\H_a:p\neq 0.45$

#We apply the one-proportion z-test to test the claim about the one population proportion.

-The sample proportion is calculated as:

$\hat p=\frac{x}{n}\\\\=\frac{20}{47}\approx0.4255$

#We determine the value of the test statistic as:

$z=\frac{\hat p-p_o}{\sqrt{\frac{p_o(1-p_o}{n}}}\\\\=\frac{0.4255-0.45}{\sqrt{(0.45\times 0.55)/47}}\\\\=-0.3376$

#We determine the p-value using the normal probability table:

$P=P(Z<-0.3376 \ or \ Z>0.3376)\\\\=2P(Z<-0.3376)\\\\=2\times 0.32636 \\\\=0.6527$

$P>0.05$ =>Fail to reject $H_o$

There is insufficient evidence to support the claim that  it's not a surprising value given that only 45​% of all its employees are women