Question

You wish to test the following claim (HaHa) at a significance level of α=0.01α0.01.

      Ho:μ=62.8Hoμ62.8
      Ha:μ>62.8Haμ62.8

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=4n4 with mean M=74.5M74.5 and a standard deviation of SD=16.7SD16.7.

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

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) αα
• greater than αα

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 62.8.
• There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 62.8.
• The sample data support the claim that the population mean is greater than 62.8.
• There is not sufficient sample evidence to support the claim that the population mean is greater than 62.8.

Answer 1

For the given claim the hypotheses are:

Ho:μ=62.8
Ha:μ>62.8

Based on the Hypothesis it will be a one-tailed test.

Given that the population is normally distributed, but do not know the standard deviation. The sample of size n=4 with mean M=74.5 and a standard deviation of SD=16.7.

Since the population standard deviation is not known hence t-distribution is applicable. Based on the sample size the degree of freedom = n-1=4-1= 3

Test statistic:

P-value:

The P-value for a t-test statistic is calculated using excel formula with the help of degree of freedom and calculated test statistic which is =T.DIST.RT(1.401, 3), thus P-value = 0.1279.

So, P-value > 0.01

Decision:

Since P-value is greater than 0.01 hence we fail to reject the null hypothesis.

Conclusion:

Since the claim is Ha hence and since we fail to reject the null Ho so, there is not sufficient sample evidence to support the claim that the population mean is greater than 62.8.