Question

A class of two hundred students took a calculus final. If the sample mean for thirty randomly selected students was 95 percent with a (sample) standard deviation of 6.6 percent, construct a 99% confidence interval for the mean score of all students. Show all work, including the formula you are using.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 95

sample standard deviation = s = 6.6

sample size = n = 200

Degrees of freedom = df = n - 1 = 199

At 99% confidence level the t is ,

t _/2,df = t_0.005,199 = 2.601

Margin of error = E = t_/2,df * (s /n)

= 2.601 * (6.6 / 200)

= 1.214

The 99% confidence interval estimate of the population mean is,

- E < < + E

95 - 1.214 < < 95 + 1.214

93.786 < < 96.214

(93.786 , 96.214)