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=0.01α=0.01.     

Ho:μ1=μ2Ho:μ1=μ2
Ha:μ1<μ2Ha:μ1<μ2

You obtain the following two samples of data.

Sample #1	Sample #2
71.2 85.7 85.4 76.5 92.2 81.3 72.7 71.8 86.8 78.3 86.3 78.7 80.3 72.2	93.3 83.2 86.8 85.3 81.6 80.5 87.8 88.6 75.4

1. What is the test statistic for this sample?
   
   test statistic = Round to 3 decimal places.
   
2. What is the p-value for this sample?
   
   p-value = Use Technology 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

Here in this scenario our claim is that claim that

Claim : The first population mean is less than the second population mean .

To test the given claim we have to use two sample t test because the population standard deviations is unknown.

Here we assumed that variances are unequal and further the test is performed as below,

First we need to find out the mean and sample Standerd deviation of both sample.

Sample 1 :

Sample 2 :

Now the test is as below,

72.2	93.3 83.2 86.8 85.3 81.6 80.5 87.8 88.6 75.4

1. What is the test statistic for this sample?
   
   test statistic = -1.911 ( Rounded to 3 decimal places.)
2. What is the p-value for this sample?
   
   p-value = 0.0352 Using Excel (Rounded to 4 decimal places.)
3. The p-value is.0.0352 > 0.01
   • greater than α
4. This test statistic leads to a decision to...
   • fail to reject the null Hypothesis at 0.01 level.

As such, the final conclusion is that...

Therefore there is not sufficient evidence to claim that the population mean of mu1 is less than second population mean mu2. At 0.01 level of significance.

Thank you.