Question

A random sample of 25 CCRI students found that the average amount spent on textbooks for a course was $180 with a standard deviation of $30. Find a 95% 2-tailed confidence interval for the population mean (μ) of the amount a CCRI student spends on textbooks.

Answer 1

Solution :

Given that,

= 180

s =30

n = Degrees of freedom = df = n - 1 =25 - 1 = 14

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

  / 2= 0.05 / 2 = 0.025

t /2,df = t0.025,24 = 2.064 ( using student t table)

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

= 2.064 * (30 / 25)

= 12.38

The 95% confidence interval mean is,

- E < < + E

180-12.38 < < 180+ 12.38

167.62 < < 192.38