Question

You wish to test the claim that the first population mean is greater than the second population mean at a significance level of α=0.005

Ho:μ1=μ2
Ha:μ1>μ2

You obtain the following two samples of data.

Sample #1	Sample #2
57.7 63.3 64.3 70.1 53.6 69.6 72.2 67.3 70.1	31.0 55.7 63.8 71.4 71.4 83.6 87.9 102.3 34.9 84.5 75.1 78.5 58.8

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) α
   • 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 greater than the second population mean.
   • There is not sufficient evidence to warrant rejection of the claim that the first population mean is greater than the second population mean.
   • The sample data support the claim that the first population mean is greater than the second population mean.
   • There is not sufficient sample evidence to support the claim that the first population mean is greater than the second population mean.

Answer 1

We will use two sample t-test to answer questions. Detailed solution is given in the images below

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