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Estimating Population Means: Confidence Intervals for Large and Small Samples, Exams of Probability and Statistics

Walters State Community CollegeProbability and Statistics

Solutions for calculating confidence intervals for population means using given sample data, both for large and small samples. It includes examples with different sample sizes, means, standard deviations, and confidence levels. Students of statistics and research methods can use this document as study notes, summaries, or exercises to understand the concept of confidence intervals and their applications.

Typology: Exams

Pre 2010

Uploaded on 08/18/2009

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Estimating a Population Mean: Large Samples
1. Find the 95% confidence interval for
if 7.3, 84.2, and 40.
x n
µ σ
= = =
2. Find the 99% confidence interval for
if s 45.5, 122, and 100.
x n
µ
= = =
3. Find the 90% confidence interval for
if s 45.5, 122, and 100.
x n
µ
= = =
4. A study of 50 shafts used in automatic transmissions shows a mean length of 3.514 cm, and a
standard deviation of 0.012 cm. Find the 99% confidence interval for
µ
.
5. A study of 300 GMAT exam scores yields a mean of 500 with a standard deviation of 55. Find
the 95% confidence interval for
µ
.
pf2

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Estimating a Population Mean: Large Samples

1. Find the 95% confidence interval for μ if σ = 7.3, x = 84.2, and n =40.

2. Find the 99% confidence interval for μ if s = 45.5, x = 122, and n =100.

3. Find the 90% confidence interval for μ if s = 45.5, x = 122, and n =100.

  1. A study of 50 shafts used in automatic transmissions shows a mean length of 3.514 cm, and a

standard deviation of 0.012 cm. Find the 99% confidence interval for μ.

  1. A study of 300 GMAT exam scores yields a mean of 500 with a standard deviation of 55. Find

the 95% confidence interval for μ.

Estimating a Population Mean: Small Samples

1. Find the 90% confidence interval for μ if s = 12.2, x = 78.8, and n =27.

  1. A study of 20 cat-tune-up times yields a mean of 100 minutes with a standard deviation of 15

minutes. Find the 80% confidence interval for μ.

  1. The manager of a restaurant finds that for 7 randomly selected days the number of customers served were: 289 326 264 318 306 269 352 Find the 90% confidence

interval for μ.

  1. In crash tests of 15 Honda Odyssey minivans, collision repair costs are found to have a distribution that is roughly bell-shaped, with a mean of $1,786 and a standard deviation of $937. Construct the 99% confidence interval for the mean repair cost in all such vehicle collisions.