Answer: (0.093,0.267)
Step-by-step explanation:
The confidence interval for the difference in proportion is given by :-
[tex](p_1-p_2)\pm z_{\alpha/2}\sqrt{\dfrac{p_1(1-p_1)}{n_1}+\dfrac{p_2(1-p_2)}{n_2}}[/tex]
Given : [tex]n_1=200[/tex]; [tex]n_2=300[/tex]
Proportion of men said they wore seatbelts =[tex]p_1=\dfrac{130}{200}=0.65[/tex]
Proportion of women said they wore seatbelts =[tex]p_2=\dfrac{140}{300}\approx0.47[/tex]
Significance level : [tex]\alpha=1-0.95=0.05[/tex]
Critical value : [tex]z_{\alpha/2}=z_{0.025}=1.96[/tex]
Now, the 95% confidence interval for the difference in proportion of men and women who wear seatbelts will be :-
[tex](0.65-0.47)\pm (1.96)\sqrt{\dfrac{0.65(1-0.65)}{200}+\dfrac{0.47(1-0.47)}{300}}\\\\\approx0.18\pm0.087\\\\=(0.093,0.267)[/tex]
Hence, the 95% confidence interval for the difference in proportion of men and women who wear seatbelts = (0.093,0.267)
Answer:
The total number of men is 32. Of these men, 25 wore a watch. So, the number of men who didn’t wear a watch is 7, because 32 − 25 = 7.
Step-by-step explanation:
