3. In a study conducted recently 667 out of 1072 people surveyed expressed prefe

Question

3. In a study conducted recently 667 out of 1072 people surveyed expressed preference for chocolate ice cream over other flavors. Let p be the proportion of the population surveyed that prefers chocolate ice cream. a) At 5% significance level do the data presents evidence that more than 60% of people from surveyed population prefer chocolate ice cream? Test appropriate hypothesis. b) obtain 95% confidence interval for p. Based on your ca, do you have evidence that p o.60? Is your answer the same as in part (a)? error in your interval from part to at most (b) to margin c) What sample size needed cut is for Use 50% as best a 196?

Explanation / Answer

SOLUTION :-

a)

Appropriate Hypothesis is given as
H0 : p =0.6

Ha : p > 0.6

z=1.484 , p-value=0.0689 >0.05 Null not rejected.

No evidence that more than 60% of the population prefers chocolate ice cream over other flavors.

b)

(0.593, 0.651) CI contains % below and above 60%.

No evidence that p > 0.6.

c)

= 0.5 (0.5) (1.96/0.01)2

= 0.25 (196)2

= 0.25 (38416)

= 9604

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