Question

You wish to test the following claim (H1H1) at a significance level of α=0.10α=0.10.

      Ho:μ=72.7Ho:μ=72.7
      H1:μ>72.7H1:μ>72.7

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=104n=104 with a mean of M=74.1M=74.1 and a standard deviation of SD=6.9SD=6.9.

What is the critical value for this test? (Report answer accurate to three decimal places.)
critical value =

What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic =

The test statistic is...

• in the critical region
• not in the critical region

This test statistic 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 greater than 72.7.
• There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 72.7.
• The sample data support the claim that the population mean is greater than 72.7.
• There is not sufficient sample evidence to support the claim that the population mean is greater than 72.7.

Answer 1

Solution:

This is a right tailed test is,

Critical value of  the significance level is α = 0.10, and the critical value for a right-tailed test is

= 1.29

The test statistics,

t = ( - )/ (s/)

= ( 74.1 - 72.7 ) / ( 6.9 / 104 )

= 2.069

Since it is observed that t = 2.069 > = 1.29, it is then concluded that the null hypothesis is rejected.

Reject the null hypothesis.

The sample data support the claim that the population mean is greater than 72.7.