Using the t-Distribution to Calculate Confidence Intervals

By Consumer Dummies

Use the t-table as needed and the following information to solve the following problems: The mean length for the population of all screws being produced by a certain factory is targeted to be

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Assume that you don’t know what the population standard deviation is. You draw a sample of 30 screws and calculate their mean length. The mean for your sample is 4.8, and the standard deviation of your sample (s) is 0.4 centimeters.

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Sample questions

  1. What is the 95% confidence interval for the population mean? Round your answer to two decimal places.

    Answer: (4.65, 4.95)

    The formula for the confidence interval for one population mean, using the t-distribution, is

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    In this case, the sample mean,

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    is 4.8; the sample standard deviation, s, is 0.4; the sample size, n, is 30; and the degrees of freedom, n – 1, is 29. That means tn 1 = 2.05.

    Now, plug in the numbers:

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    Rounded to two decimal places, the answer is 4.65 to 4.95.

  2. What is the 90% confidence interval for the population mean? Round your answer to two decimal places.

    Answer: (4.68, 4.92)

    The formula for the confidence interval for one population mean, using the t-distribution, is

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    In this case, the sample mean,

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    is 4.8; the sample standard deviation, s, is 0.4; the sample size, n, is 30; and the degrees of freedom, n – 1, is 29. That means that tn – 1 = 1.70.

    Now plug in the numbers:

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    Rounded to two decimal places, the answer is 4.68 to 4.92.

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