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 [tex]p_o=0.45, n=47, x=20[/tex]
-We state our hypothesis as:
[tex]H_o:p=0.45\\\\H_a:p\neq 0.45[/tex]
#We apply the one-proportion z-test to test the claim about the one population proportion.
-The sample proportion is calculated as:
[tex]\hat p=\frac{x}{n}\\\\=\frac{20}{47}\approx0.4255[/tex]
#We determine the value of the test statistic as:
[tex]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[/tex]
#We determine the p-value using the normal probability table:
[tex]P=P(Z<-0.3376 \ or \ Z>0.3376)\\\\=2P(Z<-0.3376)\\\\=2\times 0.32636 \\\\=0.6527[/tex]
[tex]P>0.05[/tex] =>Fail to reject [tex]H_o[/tex]
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
