Question

5. A teacher was interested in the mathematical ability of graduating high school seniors in her state. She gave a 32-item test to a random sample of 15 seniors with the following results: mean = 1270, and standard deviation = 160. Find the 95% confidence interval and write a sentence describing what it means. Show your work.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 1270

sample standard deviation = s = 160

sample size = n = 15

Degrees of freedom = df = n - 1 = 15 - 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 = t_0.025,14 = 2.145

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

= 2.145 * ( 160/ 15)

= 88.6

The 95% confidence interval estimate of the population mean is,

- E < < + E

1270 - 88.6 < < 1270 + 88.6

1181.4 < < 1358.6

(1181.4 , 1358.6)