STA 2023

Section 6.1

Confidence Intervals for the Mean (Large Samples)

Estimating Population Parameters



Critical Values





Margin of Error



 Example 2: A random sample of 120 students has a test score average with a standard deviation of 9.2. Find the margin of error if c = 0.98.

 Answer: 1.96

 Example 3: A random sample of 40 students has a mean annual earnings of $3120 and a standard deviation of $677. Find the margin of error if c = 0.95.

 Answer: $210

Confidence Intervals for the Population Mean



 Example 4: A random sample of 150 students has a grade point average with a mean of 2.86 and with a standard deviation of 0.78. Construct the confidence interval for the population mean, μ, if c = 0.98.

 Answer: (2.71, 3.01)  Interpretation: We are 98% confident that the population grade point average is between 2.71 and 3.01.

 Example 5: In a sample of 10 randomly selected women, it was found that their mean height was 63.4 inches. From previous studies, it is assumed that the standard deviation σ is 2.4 and that the population of height measurements is normally distributed. Construct the 95% confidence interval for the population mean.

 Answer: (61.9, 64.9)  Interpretation: With 95% confidence, the average height of all women is between, 61.9 inches and 64.9 inches.

 Example 6: The number of wins in a season for 32 randomly selected professional football teams are listed below. Construct a 90% confidence interval for the true mean number of wins in a season.

9 11 12 12 9 10 10 9 9 6 7 9  Answer: (7.2, 8.8) 8 4 5 7 10 11 12 10 9 9 6 7 7 8 4 7 2 8 3 5

Minimum Sample Size.

