Answer:
a) yes The assumptions and conditions necessary for inference.
b)The 95% of confidence intervals for p₁-p₂ is determined by
(-0.15523,-0.07057)
c) The sample proportion of men = 0.3931 = 39%
The sample proportion of women = 0.5061 = 50%
we observe that arthritis is more likely to afflict women than men
Step-by-step explanation:
Explanation:-
a) yes The assumptions and conditions necessary for inference.
b)
Given A survey was taken of randomly selected Americans, age 65 and older, which found that 401 of 1020 men suffered from some form of arthritis.
Given first sample size 'n₁' = 1020
First sample proportion
'p₁' =

q₁ = 1-p₁ = 1-0.3931 =0.6069
Given A survey was taken of randomly selected Americans, age 65 and older, which found that 536 of 1059 men suffered from some form of arthritis
Given second sample size 'n₂' = 1059
Second sample proportion

q = 1-p =1-0.5061 =0.4939
Step(ii):-
The 95% of confidence intervals for p₁-p₂ is determined by
![[p_(1) - p_(2) - Z_(\alpha ) S.E(p_(1) - p_(2)) ,p_(1) - p_(2) + Z_(\alpha ) S.E(p_(1) - p_(2))]](https://img.qammunity.org/2021/formulas/mathematics/college/qrszriqd53kwx7yzyb75e9ptfpxptej9sj.png)
where




Step(iii):-
The 95% of confidence intervals for p₁-p₂ is determined by
![[p_(1) - p_(2) - Z_(\alpha ) S.E(p_(1) - p_(2)) ,p_(1) - p_(2) + Z_(\alpha ) S.E(p_(1) - p_(2))]](https://img.qammunity.org/2021/formulas/mathematics/college/qrszriqd53kwx7yzyb75e9ptfpxptej9sj.png)
(0.3931-0.506 - 1.96 ×0.0216 , 0.3931-0.506 +1.96 ×0.0216)
(-0.1129-0.04233, -0.1129+0.04233)
(-0.15523,-0.07057)
Final answer:-
95% confidence interval for the difference in the proportions of senior men and women who have this disease.
(-0.15523,-0.07057)
c)
The sample proportion of men = 0.3931 = 39%
The sample proportion of women = 0.5061 = 50%
we observe that arthritis is more likely to afflict women than men