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.

Confidence Interval on the Mean

Questions

Question 1 out of 5.

You know the mean and standard deviation of the population. You take a sample from this population and compute the 90% confidence interval for the mean. This interval contains values that are within how many standard deviations of the mean?

Question 2 out of 5.

There is a population of test scores. You take a sample of 11 scores and use them to estimate the population mean and standard deviation. Then you compute a 95% confidence interval for the mean. This confidence interval contains values that are within how many standard deviations of its mean?

Question 3 out of 5.

You take a sample (N = 25) of test scores from a population. The sample mean is 38, and the population standard deviation is 6.5. What is the 95% confidence interval on the mean?

(37.49, 38.51)

(36.49, 39.51)

(35.45, 40.55)

(25.26, 50.74)

Question 4 out of 5.

You take a sample (N = 9) of heights of fifth graders. The sample mean was 49, and the sample standard deviation was 4. What is the 99% confidence interval on the mean?

(39.76, 58.24)

(44.53, 53.47)

(45.93, 52.07)

(47.51, 50.49)

Question 5 out of 5.

Based on the data below, what is the upper limit of the 95% confidence interval for the mean of A1? You may want to use the Analysis Lab or another statistical program to answer this.
________