A random sample of 92 adult is Selected from the city of Whitewater and it is fo

Question

A random sample of 92 adult is Selected from the city of Whitewater and it is found that 61 have health insurance. a. Give an estimate for the true proportion of all adults in Whitewater who have health insurance. Specify the probability distribution for this estimate. b. Find a 95% confidence interval for the true proportion of all adults in the town who have health insurance. What does this interval tell you? c. Suppose the City of Whitewater wishes to test the belief (hypothesis) that the true proportion of all adults in Whitewater who have health insurance is 80%, or P = 0.80. Is the City of Whitewater justified in this belief? Why or why not? You must base your answer on evidence.

Explanation / Answer

32)a)estimated proportion p=61/92=0.663

probabilty distribution is approximately normal as np>10 and n(1-p)>10

b)for std error =(p(1-p)/n)1/2 =0.0493

for 95% CI, z=1.96

hence confidence interval =sample proportion -/+ z*std error =0.5665 ; 0.7596

above interval gives 95% chance to contain true mean of proportion of people in city of Whitewater who have health insuarance.

c)as our interval does not contain 0.8 as probable value of true proportion, we can not accept the claim that 80% have health insuarance

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