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Chapter 8: Problem 43

For each of the following, find the area in the appropriate tail of the \(t\) distribution. a. \(t=-1.302\) and \(d f=42\) b. \(t=2.797\) and \(n=25\) c. \(t=1.397\) and \(n=9\) d. \(t=-2.383\) and \(d f=67\)

Short Answer

Expert verified
The solution to this exercise involves using a \(t\)-distribution resource to find the areas for the given \(t\) scores and degrees of freedom. The exact p-values (areas) would depend on the specific calculator or \(t\)-distribution table used.

Step by step solution

01

Interpret the given \(t\) and degrees of freedom

Firstly, observe the given values for \(t\) and either the degrees of freedom (df or n). The \(t\) score represents the calculated difference represented in units of standard error. Positive \(t\) indicates the sample mean is greater than the hypothesized population mean, whereas negative \(t\) signals the opposite. The degrees of freedom (often shown as n or df in \(t\) tests) are related to the sample size and affect the shape of the \(t\)-distribution.
02

Use a \(t\)-distribution chart or calculator

In the next step, a \(t\)-distribution chart or calculator is used to find the area in the tail. Note that if \(t\) is negative, look into the left tail of the distribution, if \(t\) is positive, look into the right tail. Enter the given \(t\) score and degrees of freedom (df or n) into your resource to find the p-value (area).
03

Repeat for each given scenario

Repeat the first two steps for each given set of \(t\) and df/n. Record the calculated area for each.

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Most popular questions from this chapter

According to the 2010 Time Use Survey conducted by the U.S. Bureau of Labor Statistics, Americans of age 15 years and older spent an average of 164 minutes per day watching TV in 2010 (USA TODAY, June 23,2011 ). Suppose a recent sample of 25 people of age 15 years and older selected from a city showed that they spend an average of 172 minutes per day watching TV with a standard deviation of 28 minutes. Make a \(90 \%\) confidence interval for the average time that all people of age 15 years and older in this city spend per day watching TV. Assume that the times spent by all people of age 15 years and older in this city watching TV have a normal distribution.

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