Question

A sample of 10 is chosen from a normal distribution with the following results :

{ 1, 5, 6, 8, 12, 16, 18, 20, 26, 28}

Test the claim that the μ < 15, that is H0 : μ = 15 & H_{1 :} μ < 15 with x = 0.01

Answer 1

Here, we have to use one sample t test for the population mean.

The null and alternative hypotheses are given as below:

H0: µ = 15 versus Ha: µ < 15

This is a lower tailed test.

The test statistic formula is given as below:

t = (Xbar - µ)/[S/sqrt(n)]

From given data, we have

µ = 15

Xbar = 14

S = 9.128709292

n = 10

df = n – 1 = 9

α = 0.01

Critical value = -2.8214

(by using t-table or excel)

t = (Xbar - µ)/[S/sqrt(n)]

t = (14 - 15)/[ 9.128709292/sqrt(10)]

t = -0.3464

P-value = 0.3685

(by using t-table)

P-value > α = 0.01

So, we do not reject the null hypothesis H0.