Suppose you plan to take a survey of Math 146 students asked about their overall grades at CBC. 22 students were surveyed, and it was found that the average GPA of the 22 sampled students was a 3.2, with a standard deviation of 0.9 points. Suppose you want to re-sample the population to reduce the margin of error. If you plan to calculate a 90% confidence interval for the true mean GPA of Math students, how many samples would be necessary to reduce the margin of error to 0.2 points?

Step-by-step explanation:

we have the data set given below here and using it, we want to find the sample mean X. Bar, the sample standard deviation S. And constructed 99% confidence interval for the population we knew, assuming the population is normally distributed. So since we have this data we can find expire and s using the appropriate definitions expire, is that some of the data divided by n 2.353 and s. Is the square root of the sum of deviations of the mean square divided by n minus one. In this case 1.3 Now with X. Bar and sample standard deviation S, we can use a student's t distribution to construct this confidence interval. So we can identify the appropriate T score. So for the degree of freedom and minus one equals 14 and critical values um providing probability 140.99 for the confidence interval,  to identify T C equals 2.977 Now, with this T. C, we can identify the margin of error E, which is given by this formula plugging in our T C. S and N. We obtain E equals 0.572 And now plugging into our confidence interval formula, which is that new falls between a sample mean minus C, and sampling plus E gives us our confidence interval. That new is between 1.781 and 2.9 to 5 with 99% confidence.

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