Complete Question
The complete question is shown on the first uploaded image
Answer:
a
[tex]\r p_w = 0.78[/tex]
b
[tex]\r p_m = 0.60[/tex]
c
[tex]0.08 \ to \ 0.28[/tex]
d
Yes, This is because on the interval the two are positive
Step-by-step explanation:
From the table the point estimate of the proportion of women who trust recommendations made on Pinterest is mathematically evaluated as
[tex]\r p_w = \frac{117}{150}[/tex]
[tex]\r p_w = 0.78[/tex]
From the table the point estimate of the proportion of men who trust recommendations made on Pinterest is mathematically evaluated as
[tex]\r p_m = \frac{102}{170}[/tex]
[tex]\r p_m = 0.60[/tex]
Generally 95% confidence interval estimate of the difference between the proportion of women and men who trust recommendations made on Pinterest is mathematically represented as
[tex]C= \r p_w - \r p_m \pm Z_{\frac{1-0.95}{2} } \sqrt{ \frac{\r p (1- \r p)}{n_w} + \frac{\r p_m (1- \r p_m)}{n_m} }[/tex]
Where
[tex]Z_{\frac{1-0.95}{2} }[/tex] is the is the z-statistic value of level of significance of a two-tail test
=> [tex]Z_{\frac{0.05}{2} } = 1.96[/tex] this is obtained from the the z-table
and [tex]n_m , n_w[/tex] are the sample size of the men and the women
So substituting values from table in the question
[tex]C= 0.78 -0.60 \pm 1.96 \sqrt{\frac{ 0.78(1-0.78)}{150} + \frac{0.60 (1-0.60)}{170} }[/tex]
[tex]C= 0.18 \pm 0.10[/tex]
So the 95% confidence interval is
[tex]0.08 \ to \ 0.28[/tex]
