Statistics Question

Question

You wish to test the following claim (HaHa) at a significance level of α=0.002α=0.002.

      Ho:μ=52.8Ho:μ=52.8 

      Ha:μ>52.8Ha:μ>52.8

You believe the population is normally distributed, but you do not know the standard deviation. You obtain the following sample of data:

data

73.2

83.3

68.7

52.9

119.3

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 52.8.
2. There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 52.8.
3. The sample data support the claim that the population mean is greater than 52.8.
4. There is not sufficient sample evidence to support the claim that the population mean is greater than 52.8.

Answer 1

Since you do not know the standard deviation, you will need to use the t-statistic. Since we are using the t-statistic, it is important to remember that we need to provide a degrees of freedom. The degrees of freedom is calculated by taking the number of samples n and subtracting 1. In this case, n = 5, so the degrees of freedom is 4. So, the corresponding t-distribution has 4 degrees of freedom.

The t-statistic (i.e. the test statistic) takes the following form:

sqrt(n) * (sample mean - μ) / (sample standard deviation)

The sample mean and the sample standard deviation can be calculated with their respective formulas (or using some statistical software such as Excel). μ = 0.58 as stated by the null hypothesis.

To determine the p-value, you can look up a t-table. You will need to match the value of your test statistic and the degrees of freedom to the table. Alternatively, you can use statistical software. Once you have the p-value, you can determine if it is greater than or less than alpha and make the choice to fail to reject or reject the null hypothesis. Finally, you can combine everything together to get the final conclusion.