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Chapter 10: Problem 39
Under what assumptions can the \(F\) distribution be used in making inferences about the ratio of population variances?
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A producer of machine parts claimed that the diameters of the connector rods produced by his plant had a variance of at most .03 inch \(^{2}\). A random sample of 15 connector rods produced by his plant produced a sample mean and variance of .55 inch and .053 inch \(^{2},\) respectively. a. Is there sufficient evidence to reject his claim at the \(\alpha=.05\) level of significance? b. Find a \(95 \%\) confidence interval for the variance of the rod diameters.
To compare the demand for two different entrees, the manager of a cafeteria recorded the number of purchases of each entree on seven consecutive days. The data are shown in the table. Do the data provide sufficient evidence to indicate a greater mean demand for one of the entrees? Use the MINITAB printout. \begin{tabular}{lcc} Day & \(\mathrm{A}\) & \(\mathrm{B}\) \\ \hline Monday & 420 & 391 \\ Tuesday & 374 & 343 \\ Wodnesday & 434 & 469 \\\ Thursday & 395 & 412 \\ Friday & 637 & 538 \\ Saturday & 594 & 521 \\ Sunday & 679 & 625 \end{tabular}.
In Exercise 2.36 the number of passes completed by Brett Favre, quarterback for the Green Bay Packers, was recorded for each of the 16 regular season games in the fall of 2006 (ESPN.com): \(^{3}\) $$ \begin{array}{lllrll} 15 & 31 & 25 & 22 & 22 & 19 \\ 17 & 28 & 24 & 5 & 22 & 24 \\ 22 & 20 & 26 & 21 & & \end{array} $$ a. A stem and leaf plot of the \(n=16\) observations is shown below: Based on this plot, is it reasonable to assume that the underlying population is approximately normal, as required for the one-sample \(t\) -test? Explain. b. Calculate the mean and standard deviation for Brett Favre's per game pass completions. c. Construct a \(95 \%\) confidence interval to estimate the per game pass completions per game for Brett Favre.
A paired-difference experiment was conducted using \(n=10\) pairs of observations. a. Test the null hypothesis \(H_{0}:\left(\mu_{1}-\mu_{2}\right)=0\) against \(H_{\mathrm{a}}:\left(\mu_{1}-\mu_{2}\right) \neq 0\) for \(\alpha=.05, d=.3,\) and \(s_{d}^{2}=.16 .\) Give the approximate \(p\) -value for the test. b. Find a \(95 \%\) confidence interval for \(\left(\mu_{1}-\mu_{2}\right)\).c. How many pairs of observations do you need if you want to estimate \(\left(\mu_{1}-\mu_{2}\right)\) correct to within .1 with probability equal to \(.95 ?\)
To test the comparative brightness of two red dyes, nine samples of cloth were taken from a production line and each sample was divided into two pieces. One of the two pieces in each sample was randomly chosen and red dye 1 applied; red dye 2 was applied to the remaining piece. The following data represent a "brightness score" for each piece. Is there sufficient evidence to indicate a difference in mean brightness scores for the two dyes? Use \(\alpha=.05\) Sample 78 9 \(\begin{array}{lrrrrrrrrr}\text { Dye 1 } & 10 & 12 & 9 & 8 & 15 & 12 & 9 & 10 & 15 \\ \text { Dye 2 } & 8 & 11 & 10 & 6 & 12 & 13 & 9 & 8 & 13\end{array}\)
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