Question

You wish to test the following claim ( H a Ha ) at a significance level of α = 0.02 α=0.02 .

Ho:μ=58.1
Ha:μ<58.1

You believe the population is normally distributed and you know the standard deviation is σ=13.3σ=13.3. You obtain a sample mean of M=55.1M=55.1 for a sample of size n=63n=63.

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...

• 1)in the critical region
• 2)not in the critical region

This test statistic leads to a decision to...

• 1)reject the null
• 2)accept the null
• 3)fail to reject the null

As such, the final conclusion is that...

• 1)There is sufficient evidence to warrant rejection of the claim that the population mean is less than 58.1.
• 2)There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 58.1.
• 3)The sample data support the claim that the population mean is less than 58.1.
• 4)There is not sufficient sample evidence to support the claim that the population mean is less than 58.1.

Answer 1

The provided sample mean is and the known population standard deviation is , and the sample size is n = 63

Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

This corresponds to a left-tailed test, for which a z-test for one mean, with known population standard deviation, will be used.

Critical Value

Based on the information provided, the significance level is α=0.02, and the critical value for a left-tailed test is

Test Statistics

The z-statistic is computed as follows:

The test statistic is...

2) not in the critical region

This test statistic leads to a decision to...

3) fail to reject the null

As such, the final conclusion is that...

4) There is not sufficient sample evidence to support the claim that the population mean is less than 58.1.

{Since it is observed that , it is then concluded that the null hypothesis is not rejected.

It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population mean μ is less than 58.1, at the 0.02 significance level.}

Graphically

Please do upvote if you are satisfied! Let me know in the comments if anything is not clear. I will reply ASAP!