Question

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

      Ho:μ=84.1Ho:μ=84.1
      Ha:μ<84.1Ha:μ<84.1

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=28n=28 with mean M=72.7M=72.7 and a standard deviation of SD=20.8SD=20.8.

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 p-value 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 less than 84.1.
• There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 84.1.
• The sample data support the claim that the population mean is less than 84.1.
• There is not sufficient sample evidence to support the claim that the population mean is less than 84.1.

Im so confused, how do I solve this?

Answer 1

Solution:

Here, we have to use one sample t test for the population mean.

Ho: μ = 84.1

Ha: μ < 84.1

This is a lower tailed test.

We are given

Level of significance = α = 0.01

Sample size = n = 28

Sample mean = Xbar = 72.7

Sample standard deviation = S = 20.8

Degrees of freedom = df = n – 1 = 28 – 1 = 27

Critical t value = -2.4727

(by using t-table)

Test statistic formula is given as below:

t = (Xbar - µ)/[S/sqrt(n)]

t = (72.7 – 84.1)/[20.8/sqrt(28)]

t = -2.9002

P-value = 0.0037

(by using t-table)

The p-value is 0.0037.

The P-value is less than α = 0.01

So, we reject the null hypothesis

This p-value leads to a decision to reject the null hypothesis.

As such, the final conclusion is that there is not sufficient evidence to warrant rejection of the claim that the population mean is less than 84.1.