Question

In a sample of 100 people in a certain city, 14 were found to have measles. (a) Is it reasonable to assume the distribution of sample proportions is approximately normal? (b) Is there compelling evidence, at a significance level of 0.05, that more than 10% of the people in this city have measles. Please show all your work.

Answer 1

a)

np = 100 * 0.14 = 14 >= 10

n(1-p) = 100 * ( 1 - 0.14) = 86 >= 10

Since np >= 10 and n(1-p) >= 10 ,

it is reasonable to assume that the distribution of sample proportion is approximately normal.

b)

H0: p = 0.10

Ha: p > 0.10

Test statistics

z = - p / sqrt( p (1 - p) / n)

= 0.14 - 0.10 / sqrt( 0.10 * 0.90 / 100)

= 1.33

Critical value at 0.05 level = 1.645

Since test statistics < 1.645, we do not have sufficient evidence to reject H0

We conclude at 0.05 level that we fail to support the claim.