Question

Suppose scores on exams in statistics are normally distributed with an unknown population mean. A sample of 26 scores is given below. Use Excel to find a 90% confidence interval for the true mean of statistics exam scores. Round your answers to one decimal place and use increasing order.

Answer 1

Explanation:

Using the formula for calculating confidence interval

CI = xbar±z×S/√n

xbar is the mean of the sample

z is the z score at 90% = 1.645

S is the standard deviation of the score

n is the sample size = 26

Since we are not given the scores, we can assume the values of our mean and standard Deviation

Let xbar = 38

S = 3.0

Substitute the given values into the formula

CI = 38±(1.645×3.0/√26)

CI = 38±(1.645×3.0/5.099)

CI = 38±(1.645×0.5884)

CI = 38±0.9678

CI = (38-0.9678, 38+0.9678)

CI = (38.0322, 38.9678)

CI = (38.0, 38.9)

Hence the 90% confidence interval for the true mean of statistics exam scores is 38.0≤p≤38.9

Note that the we will need to generate the mean and standard deviation from the data but since we are not given the required data, we had to assume the value we used in calculation.