A sample of 400 observations are made on the brand of cola purchased . Based on

ID: 3225965 • Letter: A

Question

A sample of 400 observations are made on the brand of cola purchased . Based on the sample , it is found that 249 purchases were made of brand P.

a) Give an estimate of the population proportion of people who buy brand P

b) Find a 90% confidence interval for the population proportion of purchases of brand P among cola purchases.

c) What would happen to the width of the confidence interval if the confidence level is changed to 99 % ?

d) Test whether the proportion of purchases for brand P differs from 60% at a 0.05 level of significance

a) point estimate = 249 / 400 = 0.6225

b) For 90% confidence interval z value = 1.645

CI = p + / - z * sqrt ( p * ( 1 - p) / n)

= 0.6225 + / - 1.645 * sqrt ( 0.6225 * 0.3775 / 400)

= (0.5826 , 0.6623)

c) If we changed the confidence level to 99% then interval will be ( 0.56 , 0.685)

Means lower limit will dcrease and upper limit will increase

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