Question

For each of the examples below, draw (or describe drawing) a sampling distribution around the reported mean, mark the upper and lower limits of the 95% confidence interval, and compute the mean values that correspond to those upper and lower limits.

1. Dr. Grimm collected a random sample of 30 sociology majors and administered an IQ test (σ = 15). This group had an average IQ of M = 105. Compute a 95% confidence interval to determine the population mean of psychology majors’ IQ scores.

2. According to 2016 data from the Centers for Disease Control and Prevention, the average life expectancy in the United States is 78.6 years, with an approximate standard deviation, σ, of 15 years. A random sample of 45 dead rock musicians finds an average age of death of 45.2 years. Calculate a 95% confidence interval to determine the population mean of a rock musician’s life expectancy.

3. Dr. Morris collects information on text messaging from a random sample of 50 adults ages 25 to 44. Dr. Morris finds that these individuals send or receive an average of 75 text messages per day. Using a standard deviation, σ, of 22, calculate the 95% confidence interval for the average number of texts sent by adults in this age group.

Answer 1

a) At 95% confidence interval the critical value is z_0.025 = 1.96

The 95% confidence interval for population mean is

M +/- z_0.025 *

= 105 +/- 1.96 * 15/

= 105 +/- 5.37

= 99.63, 110.37

b)

At 95% confidence interval the critical value is z_0.025 = 1.96

The 95% confidence interval for population mean is

M +/- z_0.025 *

= 45.2 +/- 1.96 * 15/

= 45.2 +/- 4.38

= 40.82, 49.58

c)

At 95% confidence interval the critical value is z_0.025 = 1.96

The 95% confidence interval for population mean is

M +/- z_0.025 *

= 75 +/- 1.96 * 22/

= 75 +/- 6.098

= 68.902, 81.098