Question

A sample of 15 from a normal population yields a sample mean of 43 and a sample standard deviation of 4.7. What is the P—value that should be used to test the claim that the population mean is less than 45? a. 0.0608 b. 0.1216 c. 0.4696 d. 0.9392 e. The P—value cannot be determined from the given information.

Answer 1

b. 0.1216

Explanation:

Given that a sample of 15 from a normal population yields a sample mean of 43 and a sample standard deviation of 4.7.

We have to check the p value for the claim that mean <45

`H_0: \mu =45\\H_a: \mu <45`

(Left tailed test for population mean)

Sample size n = 15

Sample mean = 45

Sample std dev s = 4.7

Since sample std deviation is being used, we use t test only

Std error of mean =
`(s)/(√(n) ) \\=1.214`

Mean difference = 43-45 = -2

t statistic = mean difference/std error

= -1.176

df = n-1 = 14

p value = 0.1216