Question

In a class of 25 students the average grade on a quiz is 16.85, with a sample standard deviation of 4.75. The grades are known to be normally distributed. a. Determine the standard error of the mean. b. Determine the 98% confidence interval for the class grades. c. If you wanted a narrower interval, would you increase or decrease the confidence level?

Answer 1

Given ,

Sample size = n = 25

Sample mean = = 16.85

Sample standard deviation = s = 4.75

a)

Standard error of the mean :

b)

We have to find 98% confidence interval for population mean

Since population standard deviation is not know, we have to use t interval formula.

Formula :

Where ,

is two tailed t critical value for given confidence level with df = n - 1

Confidence level = 98% = 0.98

df = 25-1 = 24

Using t table,  

Critical value = = 2.492

we have ,    = 16.85 , , = 2.492

Put values in formula, we get

c)

If confidence level decreases then critical value decreases, So margin of error decreases. Therefore, confidence interval become narrower.