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Chapter 8: Q. 29 (page 478)

The mean age for all Foothill College students for a recent Fall term was 33.2. The population standard deviation has been pretty consistent at 15. Suppose that twenty-five Winter students were randomly selected. The mean age for the sample was 30.4. We are interested in the true mean age for Winter Foothill College students. Let X=the age of a Winter Foothill College student.

As a result of your answer to Exercise 8.26, state the exact distribution to use when calculating the confidence interval.

Short Answer

Expert verified

The distribution is Normal Distribution.

Step by step solution

01

Given Information

The mean age for all Foothill College students for a recent Fall term was 33.2. The population standard deviation has been pretty consistent at 15. The mean age for the sample was30.4

02

Explanation

The mean is the average of a data set. The sample mean symbol is X¯, pronounced “x bar”. The sample mean is an average value found in a sample.

Normal distribution is a probability distribution that is symmetric about the mean, indicating that data around the mean are more frequent in occurrence than data far from the mean.

The answer to Exercise 8.26defines the random variable x¯which is the sample mean. The exact distribution used to calculate the confidence interval for the sample mean is Normal distribution.

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The mean age for all Foothill College students for a recent Fall term was 33.2. The population standard deviation has been pretty consistent at 15. Suppose that twenty-five Winter students were randomly selected. The mean age for the sample was 30.4. We are interested in the true mean age for Winter Foothill College students. Let X=the age of a Winter Foothill College student.

In words, define the random variable X¯.
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