Question

# You wish to test the following claim (Ha) at a significance level of α=0.10.       Ho:μ=56.1       Ha:μ≠56.1...

You wish to test the following claim (Ha) at a significance level of α=0.10.

Ho:μ=56.1

Ha:μ≠56.1

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=9 with mean M=53.6 and a standard deviation of SD=5.1.

What is the p-value for this sample? (Report answer accurate to four decimal places.)
p-value =

The p-value is...?

• less than (or equal to) α OR
• greater than α

This p-value leads to a decision to...?

• reject the null
• accept the null
• fail to reject the null

As such, the final conclusion is that...?

• There is sufficient evidence to warrant rejection of the claim that the population mean is not equal to 56.1.
• There is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to 56.1.
• The sample data support the claim that the population mean is not equal to 56.1.
• There is not sufficient sample evidence to support the claim that the population mean is not equal to 56.1.

Solution :

This is the two tailed test .

Test statistic = t

= ( - ) / s / n

= (53.6 - 56.1) /5.1 / 9

= -1.47

P(z < -1.47) = 0.0708

df = 8

P-value = 0.1798 = 0.10

P-value > Fail to reject the null hypothesis .

There is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to 56.1.