Question

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

      Ho:μ=88.1Ho:μ=88.1
      Ha:μ<88.1Ha:μ<88.1

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=33n=33 with mean M=85.9M=85.9 and a standard deviation of SD=18.2SD=18.2.

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 less than 88.1.
• There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 88.1.
• The sample data support the claim that the population mean is less than 88.1.
• There is not sufficient sample evidence to support the claim that the population mean is less than 88.1.

Answer 1

Here in this scenario to test the given Hypothesis we have to use one sample t test because here the population standard deviations is unknown.

Further the one sample t test is performed at 0.01 level of significance as below,

The t critical value is calculated using t table or using Excel at 32 degrees of freedom.

The test Statistic tcal = -0.694.

The p value is 0.2462.

Conclusion :

Since p value is 0.2462 which is greater than alpha level of significance 0.01.

So we fail to Reject Ho null hypothesis and concluded that There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 88.1.

At 0.01 level of significance our result is not significant.

Thank you.