An accounting professor is notorious for being stingy in giving out good letter grades. In a large section of 140 students in the fall semester, she gave out only 5% As, 23% Bs, 42% Cs, ad 30% Ds and Fs. Assuming that this was a representative class, compute a 95% confidence interval for the proportion of students that obtain a letter grade of B or better from this professor. Interpret your confidence interval. (16 points)

The 95% confidence interval for the proportion of students that obtain a letter grade of B or better from this professor is (0.2056, 0.3544). The interpretation is that we are 95% sure that the true proportion of students who obtain a letter grade of B or better from this professor is between 0.2056 and 0.3544.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of , and a confidence level of , we have the following confidence interval of proportions.

In which

z is the zscore that has a pvalue of .

For this problem, we have that:

140 students, so

B or better are grades of A or B.

5% earn As, 23% earn Bs, so

95% confidence level

So , z is the value of Z that has a pvalue of , so .

The lower limit of this interval is:

The upper limit of this interval is:

The 95% confidence interval for the proportion of students that obtain a letter grade of B or better from this professor is (0.2056, 0.3544). The interpretation is that we are 95% sure that the true proportion of students who obtain a letter grade of B or better from this professor is between 0.2056 and 0.3544.

a

step-by-step explanation: