Question

The Director of Marketing has supplied the analyst with only enough funding for a survey of 900 cereal consumers. In this sample, she finds 270 consumers who indicate that they only purchase organic cereals. This results in a 95% confidence interval given by [.270, .330]. For her presentation of the survey results to the Director, which of the following would be an appropriate interpretation of the confidence interval she has computed? Mark the statement with “A” if appropriate, and “NA” if not appropriate.

_____The margin of error of .03 indicates how much the sample proportion differs from the population proportion.

_____I cannot be sure that the value of the population proportion is somewhere in the interval [.270, .330].

_____Using a larger sample size would result in an interval that has a higher level of confidence.

_____The interval I have computed from the results of the survey provides evidence that supports the claim that the population proportion of cereal consumers who buy only organic cereals is greater than .25.

_____The probability that the population proportion is within the interval [.270, .330] is .95. The margin of error for the analyst’s interval is .03. Why is the margin of error for her interval larger than the margin of error of .025 that she had originally intended for the interval as stated in part (a)? ONE SENTENCE MAXIMUM; BE SPECIFIC.

Answer 1

The margin of error indicates the maximum difference between the sample and population proportions. So, the statement is applicable.

The confidence interval is expected to contain the exact value of the population parameter with a certain probability. The 95% confidence interval will contain the population parameter with probability 0.95. So, the statement is applicable.

Increasing the sample size increases the accuracy of the confidence interval and so it increases confidence. So, the statement is applicable.

Since, the ontained interval does not contain the value 0.25 and 0.25 is less than the values in the confidence interval, the interval computed from the results of the survey provides evidence that supports the claim that the population proportion of cereal consumers who buy only organic cereals is greater than .25. So, the statement is applicable.