Math Question 3

Question

You measure 29 randomly selected textbooks' weights, and find they have a mean weight of 53 ounces. Assume the population standard deviation is 12.4 ounces. Based on this, construct a 95% confidence interval for the true population mean textbook weight.

Give your answers as decimals, to two places

Answer 1

First, figure out what the problem is asking:

1. Confidence interval of a mean.

Next examine what information you have been given:

1. sample mean = 53 ounces
2. population standard deviation assumed known. 12.4 ounces.
3. N = 29.
4. population standard deviation is known, but, technically, we should use a t-test because the sample size is < 30. Let's run both a Z and a single sample t-test and compare the results!
5. calculate the standard error: sigma/sqrt(N) = 12.4/sqrt(29) = 2.228
6. The critical value for a 95% confidence interval for Z = 1.96
7. The critical value for a 95% confidence interval for t on N -1 = 28 degrees of freedom = 2.048

CI95 using z scores = 53 +- 1.96*2.228 = 53 +- 4.3669

CI95 using t scores = 53 +- 2.048*2.228 = 53 +- 4.5629

The t-score-based interval is only very slightly wider than that based on the z score.