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# What is the Standard Error of the mean difference?

INSTRUCTIONS TO CANDIDATES
###### ANSWER ALL QUESTIONS

We want to know if American’s and Canadian’s have the same average height. We observe 8 Americans and 8 Canadian’s and measure their heights in inches. Perform a difference of means hypothesis test and tell me what your results say with respect to the null hypothesis. (Remember you have to calculate the variance for each variable using the equation with n-1 in the denominator). IF YOU SO CHOOSE, YOU CAN DO ALL THE CALCULATIONS IN R. As you can see there are no points for the intermediate calculation steps and all that really counts is getting the null and alternative hypothesis correct and the conclusion of the hypothesis tests.

1 70 68

2 68.5 66

3 64.5 65

4 72 69

5 70 62

6 66 66

7 68 67

8 70 65

sums

mean

variance

1) State the Null and Alternative Hypotheses. (5 points)

2) Establish your decision criteria and determine t critical (df = N1+N2-2).

3) What is the Standard Error of the mean difference?

4) Calculate t calculated?

5) Are the results statistically significant (i.e., can we reject the null hypothesis). Make sure to give the full answer in terms of the question being investigated in the current example. (20points).

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