Confidence Intervals for the Mean
This section explains the need for confidence intervals and why a confidence interval is not the probability the interval contains the parameter. Then, it discusses how to compute a confidence interval on the mean when sigma is unknown and needs to be estimated. It also explains when to use t-distribution or a normal distribution. Next, it covers the difference between the shape of the t distribution and the normal distribution and how this difference is affected by degrees of freedom. Finally, it explains the procedure to compute a confidence interval on the difference between means.
Difference between Means
Questions
Question 1 out of 4.
Select all of the assumptions that you need to make when creating a confidence interval on the difference between means.
At least 2% of the population sampled
Independently sampled values
Homogeneity of variance
Normally distributed populations
Question 2 out of 4.
You are comparing men and women on hours spent watching TV. You pick a sample of 12 men and 14 women and calculate a confidence interval on the difference between means. How many degrees of freedom does your t value have?
Question 3 out of 4.
You are comparing freshmen and seniors at your college on hours spent
studying per day. You pick a sample of 11 people from each group. For
freshmen, the mean was 3 and the variance was 1.2. For seniors, the mean
was 2 and the variance was 1. Calculate a 90% confidence interval on
the difference between means (freshmen - seniors). What is the lower
limit of this CI?Question 4 out of 4.
Scores on a test taken by 1st graders and 2nd graders were compared to look at development. The five 1st graders sampled got the following scores: 4, 3, 5, 7, 4. The five 2nd graders sampled got the following scores: 7, 9, 8, 6, 9. Compute the 95% confidence interval for the difference between means (2nd graders - 1st graders). You may use the Analysis Lab. What is the upper limit?
Grade Score 1 4 1 3 1 5 1 7 1 4 2 7 2 9 2 8 2 6 2 9