Question

A college admissions officer takes a simple random sample of 100 entering freshmen and computes their mean mathematics SAT score to be 458. It is know that the population standard deviation of all mathematics SAT scores is 116. a. What function would you use to create a confidence interval for the mean mathematics SAT score for the entering freshman class? b. Create a 99% confidence interval for the mean mathematics SAT score for the entering freshman class. Round to 2 decimal places. ( C. Based on the confidence interval just created, is it likely that the mean mathematics SAT score for the entering freshman is greater than 500?

Answer 1

a)
As the populatiion variance is hence we'll be using the Z-test statistic fucntion to compute the confidence interval assuming the population is a normal population.
b)
Calculations:


c)
As the value 500 doesn't lie inside our 99% confidence interval hence its unlikely for the mean math score to be greater than 500.

We need to construct the 99% confidence interval for the population mean u. The following information is provided: Sample Mean X = 458 Population Standard Deviation (0) = 116 Sample Size (N) = 100 The critical value for a = 0.01 is ze = 21-a/2 = 2.576. The corresponding confidence interval is computed as shown below: o o CI X - 2c X X + Zcx vn vn 116 116 458 – 2.576 458 + 2.576 V100 = (428.12, 487.88) Therefore, based on the data provided, the 99% confidence interval for the population mean is 428.12 < p < 487.88, which indicates that we are 99% confident that the true population mean u is contained by the interval (428.12, 487.88).