A teacher wants to compare the mean geology scores of two different classes. She is testing the null hypothesis that there is no difference in the population mean scores of the two classes. The difference of the sample means is 51.4. If the standard deviation of the distribution of the difference of sample means is 16.66, what is the 95% confidence interval for the population mean difference?
Please see the first Related Question below.
To find the 95% confidence interval for the population mean difference, we will use the formula:
Confidence Interval = (Difference of sample means) ± (Critical value × Standard deviation of the distribution of the difference of sample means)
The critical value for a 95% confidence interval is typically obtained from the standard normal distribution, where the area under the curve to the left of the critical value is 0.025. The corresponding critical value is approximately 1.96.
Let's calculate the confidence interval:
Confidence Interval = (51.4) ± (1.96 × 16.66)
First, multiply the critical value by the standard deviation:
1.96 × 16.66 ≈ 32.5856
Now, add and subtract the result from the difference of sample means:
51.4 + 32.5856 ≈ 84.9856
51.4 - 32.5856 ≈ 18.8144
Therefore, the 95% confidence interval for the population mean difference is approximately (18.8144, 84.9856).