Question

Aa random sample of 100 students is taken from a larger population of students in a multi-lecture course and the sample mean (average) of their final grades is found to be 63.25. suppose it is known that the population standard deviation is 3.4. you wish to determine whether the average grade for the population differs from 62. use r to get the needed z critical value and then create a 99% z confidence interval for the average final grade for the population by hand. choose the correct statement below.

a. The Zα/2 (found from R) used to calculate the 96% confidence interval is 2.053749.
b. The Zα/2 (found from R) used to calculate the 96% confidence interval is 0.02.
c. The Zα/2 (found from R) used to calculate the 96% confidence interval is 1.750686.
d. The Zα/2 (found from R) used to calculate the 96% confidence interval is 2.326348.

Answer 1

To construct a 99% confidence interval for the average final grade, one must obtain the correct z critical value, which is approximately 2.576, not the values listed in the choices. The interval is then calculated using the formula: sample mean +/- (z critical value * (population standard deviation / sqrt(sample size))).

Step-by-step explanation:

You are attempting to construct a 99% confidence interval around the sample mean of final grades using the population standard deviation, which is a common statistical procedure in inferential statistics. To do so, we need the z critical value for a 99% confidence interval, which can be obtained using statistical software like R, as well as the population standard deviation and the sample mean.

The confidence interval is calculated using the formula: sample mean ± (z critical value * (population standard deviation / √n)), where n is the sample size. The provided standard deviation is 3.4, and the sample mean is 63.25 with a sample size of 100. The z critical value for a 99% confidence interval can be found using R or a z-table. Typically, this value is approximately 2.576, not the values provided in the multiple-choice options, which seem to be incorrect as they relate to different confidence levels (for example, 2.326348 is close to the correct z critical value for a 98% confidence interval, not 99%).

Note: The correct z critical value for a 99% confidence interval is approximately 2.576, not any of the values given in the options a, b, c, or d. Once the correct z critical value is obtained, the confidence interval can be computed by multiplying this value by (3.4 / √100) and then adding and subtracting this amount from the sample mean of 63.25.