Question

Consider the following hypotheses and the sample data in the accompanying table. Answer the following questions using α ​=0.10.

9

8

8

8

7

8

9

11

13

7

5

8

9

8

11

Upper H0​: μ=10

Upper H1​: μ≠10

a.	What conclusion should be​ drawn?
b.	Use technology to determine the​ p-value for this test.

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 = 10 versus Ha: µ ≠ 10

This is a two tailed test.

The test statistic formula is given as below:

t = (Xbar - µ)/[S/sqrt(n)]

From given data, we have

µ = 10

Xbar = 8.571428571

S = 1.988980632

n = 14

df = n – 1 = 13

α = 0.10

Critical value = - 1.7709 and 1.7709

(by using t-table or excel)

t = (Xbar - µ)/[S/sqrt(n)]

t = (8.571428571 - 10)/[ 1.988980632/sqrt(14)]

t = -2.6874

P-value = 0.0186

(by using t-table)

P-value < α = 0.05

So, we reject the null hypothesis

There is not sufficient evidence to conclude that the population mean is equal to 10.