STA 2023Section 6.1Confidence 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 9 9 8 10 9 7 211 10 6 4 11 9 8 812 10 7 5 12 6 4 312 9 9 7 10 7 7 5

Answer: (7.2, 8.8)

Minimum Sample Size.