A survey was taken of randomly seeded Americans age 65 and o

A survey was taken of randomly seeded Americans, age 65 and older which found that 409 of 1003 men and 550 of 1063 women suffered from some form of atheist. Are the assumptions and conditions necessary tor inference satisfied? Explain Create a 95% confidence interval tor the difference in the proportions of senior men and women who haw this disease Interpret your interval in this context

Solution

a. yes the assumptions are satisfied since , majolrity of both men and women are suffering from arthritis

b. frst find mean =

502, 532(men , women)

compute the standard deviation = 100

Compute the standard error by dividing the standard deviation by the square root of the sample size: 100/sqrt(1003)) = 3.15

100/sqrt(1063) =3.067

Compute the margin of error by multiplying the standard error by 2. 3.15 x 2 = 6.30

Compute the margin of error by multiplying the standard error by 2. 3.06 x 2 = 6.12

Compute the confidence interval by adding the margin of error to the mean from Step 1 and then subtracting the margin of error from the mean:
=> 502 +6.30 , 502-6.30 (for men)

and 532 +6.12 , 532 -6.12 (from women)

c.Therefore, the arthritis effect (difference) for men is likely to be between 508.30 and 495.7

and for women between 538.12,525.88

d. yes arthritis affects more women then men , since percentage of women suffering are pretty high.