Question

# You wish to test the following claim (HaHa) at a significance level of α=0.001 Ho:μ1=μ2 Ha:μ1≠μ2...

You wish to test the following claim (HaHa) at a significance level of α=0.001

Ho:μ1=μ2
Ha:μ1≠μ2

You believe both populations are normally distributed, but you do not know the standard deviations for either. And you have no reason to believe the variances of the two populations are equal You obtain a sample of size n1=13 with a mean of ¯x1=69.1 and a standard deviation of s1=15.5 from the first population. You obtain a sample of size n2=22 with a mean of ¯x2=64.3 and a standard deviation of s2=14.4 from the second population.

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

The statistical software output for this problem is: From above output:

Test statistic = 0.9086

p - Value = 0.3726

Greater than α

Fail to reject the null

Final conclusion: There is not sufficient sample evidence to support the claim that the first population mean is not equal to the second population mean. Option D is correct.

Two sample T summary hypothesis test: Mean of Population 1 He Mean of Population 2 H.-H.: Difference between two means HOH-H=0 HH - H2=0 (without pooled variances) Hypothesis test results: Difference Sample Diff. Std. Err. DF T-Stat 4.8 5.2826342 23.821031 0.90863759 P-value 0.3726

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