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Answer:
The 90% confidence interval for the difference between means is (4.189, 8.011).
The point estimate is the difference between sample means and has a value of Md=6.1.
Step-by-step explanation:
We have to calculate a 90% confidence interval for the difference between means.
The sample 1 (American students), of size n1=12 has a mean of 69.4 and a standard deviation of 2.79.
The sample 2 (non-American students), of size n2=17 has a mean of 63.3 and a standard deviation of 3.22.
The difference between sample means is Md=6.1.
The estimated standard error of the difference between means is computed using the formula:
The critical t-value for a 90% confidence interval is t=1.703.
The margin of error (MOE) can be calculated as:
Then, the lower and upper bounds of the confidence interval are:
The 90% confidence interval for the difference between means is (4.189, 8.011).