Answer to Question #169486 in Statistics and Probability for Sunera

Question

A random sample of 25 was drawn from a normal distribution whose standard deviation is 5.

The sample mean was 80.

a) Determine the 95% confidence interval estimate of the population mean.

b) Repeat part (a) with a sample size of 100.

c) Repeat part (a) with a sample size of 400.

d) Describe what happens to the confidence interval estimate when the sample size increases.

Answer 1

The Confidence Interval formula is $\overline{X}\pm Z\frac{s}{\sqrt{n}}$ where

• X is the mean (80)
• Z is the Z-value (for 95% it equals 1.960)
• s is the standard deviation (5)
• n is the number of observations

a) 80 ± 1.96 (78 to 82)

b) 80 ± 0.98 (79 to 81)

c) 80 ± 0.49 (79.5 to 80.5)

d) Increasing the sample size decreases the width of confidence intervals, because it decreases the standard error