Test Statistic and Critical Value

Question

You wish to test the following claim (HaHa) at a significance level of α=0.005α=0.005.

      Ho:μ=56.8Ho:μ=56.8 

      Ha:μ>56.8Ha:μ>56.8

You believe the population is normally distributed and you know the standard deviation is σ=10.8σ=10.8. You obtain a sample mean of M=58.2M=58.2 for a sample of size n=58n=58.

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...

1. less than (or equal to) αα
2. greater than αα

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 greater than 56.8.
2. There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 56.8.
3. The sample data support the claim that the population mean is greater than 56.8.
4. There is not sufficient sample evidence to support the claim that the population mean is greater than 56.8.

Answer 1

For this situation you can utilize the z-statistic (standardized normal distribution).

z statistic = (sample mean - population mean)/(population standard deviation/sample size**0.5), where sample size = 58, sample mean =58.2, population mean = 56.8, population standard deviation = 10.8

The p-value is P(Z > z-statistic). It is compare to alpha = 0.005. If the p-value is less than 0.005, then the null hypothesis is rejected, otherwise it is not rejected.

If the null hypothesis is rejected, then the sample data support the claim that the population mean is greater than 56.8, otherwise, there is not sufficient sample evidence to support the claim that the population mean is greater than 56.8.