1) In a study conducted recently 671 out of 1,070 people surveyed expressed pref
ID: 3220703 • Letter: 1
Question
1) In a study conducted recently 671 out of 1,070 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 1% significance level does the data present evidence that more that 60% of the population surveyed prefer chocolate ice cream?
b) Obtain and interpret 99% confidence interval. Do you think p>0.6?
c) What sample size is needed to cut margin of margin of error in your confidence interval to at most 2%, use 50% as a best guess for p.
Explanation / Answer
here null hypothesis :Ho: p<=0.60
alternate hypothesis :Ha:p>0.60
a) for std error =(p(1-p)/n)1/2 where n=1070
=0.015
phat=671/1070=0.627
hence test stat z=(phat-p)/std error=1.8097
for 1% level ; critical value =2.326
as our test stat does not fall in critical region; we can not reject null hypothesis.
b) here phat=671/1070=0.627
std error=(phat(1-phat)/n)1/2=0.0148
99% CI; z=2.5758
confidence interval =sample proportion -/+ z*std error =0.589 ; 0.665
as our confidence interval;contains value lower then 0.6 we can not accept that p>0.6
c) for marginj of error =0.02
for 99% CI, z=2.5758
p=0.5
hence sample size =p(1-p)(z/E)2 =4147
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