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STA 2023

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.

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STA 2023

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  1. STA 2023 Section 6.1 Confidence Intervals for the Mean (Large Samples)

  2. Estimating Population Parameters

  3. Critical Values

  4. Margin of Error

  5. 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

  6. Confidence Intervals for the Population Mean

  7. 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.

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

  9. Minimum Sample Size.

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