Question

10) In a random sample of 450 people aged 20-24, 22% were smokers, random sample of 400 people aged 25-29, 16% were smokers. a) (4 points) When constructing a confidence interval for the difference between the population proportions of smokers, what must be true in order for the standard normal distribution to be used as an approximation? Show your work please b) (3 points) Construct a 95% confidence interval for the difference between the population proportions of c) (3 points) What does the confidence interval suggest about the proportion of smokers aged 20-24 compares to the proportion of smokers aged 2-297 Circle one. The proportion of smokers aged 20-24 is less than the proportion of smokers aged 25-29 A) B) The proporion of smokers aged 20-24 s greater than the proportion of smokers eged 25-29 There is not a significance difference in the proportion of smokers aged 20-24 and the proportion of smokers aged 25-29. C)

Answer 1

a)

n * p for both sets should be > 5

450 * 0.22 > 5

Also,

400 * 0.16 > 5

Thus, satisfied

b) So,

Interval is {0.0053, 0.1137}

c) As, interval does not contain zero,

we can say option B is right