In each of the following situations, state which interval estimate is appropriat

Question

In each of the following situations, state which interval estimate is appropriate (you can use names of Tl functions or write down the formula to indicate the intervals you would use). Show work by indicating different assumptions that you check. DO NOT compute the confidence interval. A random sample of 20 WKU students is collected and the number of credit cards students have is recorded. The sample mean is computed to be 2.6 and the sample standard deviation is 1.3. Assume that the number of siblings follow Normal distribution. i) Construct a 90% confidence interval for the mean number of credit cards WKU students have. ii) Construct an interval to predict the number of credit cards of a future WKU student with 90% confidence. We are interested in estimating the proportion of WKU students who have financial aid (FA). A random sample of 80 students shows that 30 students have FA. Construct a 90% confidence interval for the proportion of all WKU students who have FA. A random sample of 45 students at a high school is collected and their GPA is recorded. The sample mean is computed to be 2.5 with a sample standard deviation of 1.3. i) Construct a 95% confidence interval for the mean GPA of all students at this school. For part (i), do not assume that GPA follows Normal distribution. ii) Construct an interval that is likely to include at least 90% of possible GPA values of students at this school with 95% confidence. For this part (ii), assume that the GPA follows Normal distribution.

Explanation / Answer

1)

margin of error = z-score * std/sqrt(n)

= 1.645 * 1.3/sqrt(20)

= 0.4782

confidence interval [ 2.6 - 0.4782 , 2.6 + 0.4782] which is [ 2.1218 , 3.0782]

ii)

for future one can say with 90% confidence that it will be in the interval [ 2.1218 , 3.0782]

2)

proportion p = 30/80 = 3/8

standard error = sqrt(p * (1-p)/n)

= sqrt( 3/8 * 5/8 * 1/80 )

= 0.05413

margin of error = 0.05413 * 1.645

= 0.089

confidence interval is [ 0.286 , 0.464]

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