Question

You wish to test the claim that the first population mean is less than the second population mean at a significance level of α=0.001α=0.001.     

Ho:μ1=μ2Ho:μ1=μ2
Ha:μ1<μ2Ha:μ1<μ2

You obtain the following two samples of data.

Sample #1	Sample #2
41.5 47.1 71.9 67.8 57.1 72.9 52.3 70.3 65.5	68.8 66.2 69.3 70.4 87.8 79.7 89.4 81.0 70.4 71.4 68.8 91.6 82.1 79.1

1. What is the test statistic for this sample?
   
   test statistic =  Round to 4 decimal places.
   
2. What is the p-value for this sample?
   
   p-value =  Round to 4 decimal places.
   
3. The p-value is...
   • less than (or equal to) αα
   • greater than αα
   
   
4. This test statistic leads to a decision to...
   • reject the null
   • accept the null
   • fail to reject the null
   
   
5. As such, the final conclusion is that...
   • There is sufficient evidence to warrant rejection of the claim that the first population mean is less than the second population mean.
   • There is not sufficient evidence to warrant rejection of the claim that the first population mean is less than the second population mean.
   • The sample data support the claim that the first population mean is less than the second population mean.
   • There is not sufficient sample evidence to support the claim that the first population mean is less than the second population mean.

Answer 1

Ans.

First we test for equality of variances-

We test using R:-

Since, P-value = 0.3275 > α=0.001

Hence we fail to reject H0

And, we use t -test using equal variances

We test using R:-

Hypothesis:-

H0: μ1 = μ2
Ha: μ1 < μ2

Test Statistics:-

t = -3.8316

P-value:-

P-value = 0.0005

Decision:-

Since, P-value = 0.0005 < α=0.001

This test statistic leads to a decision to...

• reject the null

As such, the final conclusion is that...

• There is not sufficient evidence to warrant rejection of the claim that the first population mean is less than the second population mean.