Question

(b) The Foodmart Board has reviewed the cost of the basket in 2008 and deemed that up to $190 is acceptable, but that anything over $190 is excessively expensive. You wish to estimate the proportion of all supermarkets in the Foodmart chain falling into the “excessive” category. From the sample of 150 stores, we have calculated that the sample proportion of stores classified as “excessive” is, p = 10.67%.

(i) Calculate the 95% confidence interval estimate of the proportion of all supermarkets in the Foodmart chain in the “excessive” category.

2. (ii) The Foodmart Board has publicly admitted that some stores are excessively priced, but that the proportion is only 5%. Do you have any evidence to contradict this claim? Explain your answer.

3. (iii) If a 99% confidence interval was used instead of a 95% confidence interval would you have come to the same conclusion in part (ii)? Explain your answer. [Note: No calculations required]

Answer 1

b. i. z value for 95% CI is 1.96 as P(-1.96<z<1.96)=0.95

So Margin of Error is

Hence CI is

ii. Yes we do have evidence to contradict the claim as 0.05 is not in the range.

iii. For 99% CI z value is 2.576 as P(-2.576<z<2.576)=0.99

So Margin of Error is

Hence CI will be

Now 0.05 is in the range, so conclusion changes. and we do not have evidence to contradict the claim.