Posted by **moneta** on Wednesday, April 24, 2013 at 11:15am.

We want a confidence interval for the mean IQ of all the 7th grade girls in that school district. We do not know the population standard deviation so we use the confidence interval that uses the t. In order to use the t-interval we need to assume that the variable IQ has a normal distribution.

1. An important condition is that these 31 girls are an ______ of all seventh-grade girls in the school district.

2. Produce a histogram for IQ and tell me how you feel about using the t confidence interval or the t test.

a. I am terribly worried the distribution is very skewed and the sample size is very small, I should not use the t.

b. It is OK to use the t, the distribution is fairly symmetric, except for an outlier in the lower tail, but the sample size is not too small thus I trust the robustness of the t-procedure.

c. I should be using the formula for proportions instead.

3. Use STAT > Basic Statistics > 1 sample t to get a 95% confidence interval for the population mean. We get the following interval __________. Which of these interpretations is closest to the truth?

a. 95% of all the girls in 7th grade in the school district have an IQ between 100.6 and 111.07.

b. 95% of the 31 girls in the sample have an IQ between 100.60 and 111.07.

c. We are 95% confident that the mean IQ of all the girls in 7th grade in the school district is between 100.60 and 111.07.

d. There is a 0.95 probability that all the girls in the 7th grade school district have an IQ between 100.60 and 111.07.

e. We are 95% confident that the mean IQ for the 31 girls in the sample is between 100.60 and 111.07.

4. Imagine we want to test the hypothesis that H0: µ = 100 vs. Ha: µ ≠ 100 using α = 0.05. Use the confidence interval to make a decision about the null hypothesis.

a. We can’t use the confidence interval to a make a decision.

b. We would reject the null hypothesis because the 100 is not in the confidence interval.

c. We would NOT reject the null hypothesis.

d. I don’t have a p-value so I can’t make a decision.

5. How would you describe the situation in the previous question?

a. It is a clear case of statistical significance and practical significance, the population mean is very far from 100.

b. This is likely to be a case of statistical significance, because we reject the null hypothesis, but not of practical significance because the lower end of the interval 100.6 is quite close to 100.

c. This is a clear case of practical significance but not statistical significance.