91Ó°ÊÓ

The following data represent the time, in minutes, that a patient has to wait during 12 visits to a doctor's office before being seen by the doctor: $$\begin{array}{llllll}17 & 15 & 20 & 20 & 32 & 28 \\\12 & 26 & 25 & 25 & 35 & 24\end{array}$$ Use the sign test at the 0.05 level of significance to test. the doctor's claim that the median waiting time for her patients is not more than 20 minutes before being admitted to the examination room.

It is claimed that a new diet will reduce a person's weight by 4.5 kilograms, on average, in a period of 2 weeks. The weights of 10 women who followed this diet were recorded before and after a 2 -week period yielding the following data: $$\begin{array}{ccc}\text { Woman } & \text { Weight Before } & \text { Weight After } \\\\\hline 1 & 58.5 & 60.0 \\\2 & 60.3 & 54.9 \\\3 & 61.7 & 58.1 \\\4 & 69.0 & 62,1 \\\5 & 64.0 & 58.5 \\\6 & 62.6 & 59.9 \\\7 & 56.7 & 54.4 \\\8 & 63.6 & 60.2 \\\9 & 68.2 & 62.3 \\\10 & 59.4 & 58.7 \end{array}$$ Use the sign test at the 0.05 level of significance to test the hypothesis that the diet reduces the median weight by 4.5 kilograms against the alternative hypothesis that the median difference in weight is less than 4.5 kilograms.

Two types of instruments for measuring the amount of sulfur monoxide in the atmosphere are being compared in an air-pollution experiment. The following readings were recorded daily for a period of 2 weeks: $$\begin{array}{ccc} & \multicolumn{2}{c} {\text { Sulfur Monoxide }} \\\\\cline { 2 - 4 } \text { Day } & \text { Instrument } A & \text { Instrument } B \\\\\hline 1 & 0.96 & 0.87 \\\2 & 0.82 & 0.74 \\\3 & 0.75 & 0.63 \\\4 & 0.61 & 0.55 \\\5 & 0.89 & 0.76 \\\6 & 0.64 & 0.70 \\ 7 & 0.81 & 0.69 \\\8 & 0.68 & 0.57 \\\9 & 0.65 & 0.53 \\\10 & 0.84 & 0.88 \\\11 & 0.59 & 0.51 \\\12 & 0.94 & 0.79 \\\13 & 0.91 & 0.84 \\ 14 & 0.77 & 0.63\end{array}$$ Using the normal approximation to the binomial distribution, perform a sign test to determine whether the different instruments lead to different results. Use a 0.05 level of significance.

A cigarette manufacturer claims that the tar content of brand \(B\) cigarettes is lower than that of brand \(A\). To test this claim, the following determinations of tar content, in milligrams, were recorded: $$\begin{array}{l|llllll}\text { Brand } A & 1 & 12 & 9 & 13 & 11 & 14 \\\\\hline \text { Brand } B & 8 & 10 & 7 & & &\end{array}$$ Use the rank-sum test with \(\alpha=0.05\) to test whether the claim is valid.

To find out whether a new serum will arrest leukemia, 9 patients, who have all reached an advanced stage of the disease, are selected. Five patients receive the treatment and four do not. The survival times, in years, from the time the experiment; commenced are $$\begin{array}{l|ccccc}\text { Treatment } & 2.1 & 5.3 & 1,1 & 4.6 & 0.9 \\\\\hline \text { No treatment } & 1.9 & 0.5 & 2.8 & 3.1 &\end{array}$$ Use the rank-sum test. at the 0.05 level o( significance, to determine if the: serum is effective.

A consumer panel tests 9 brands of microwave ovens for overall quality. The ranks assigned by the panel and the suggested retail prices are as follows: $$\begin{array}{ccc} & \text { Panel } & \text { Suggested } \\\\\text { Manufacturer } & \text { Rating } & \text { Price } \\\\\hline A & 6 & \mathrm{~S} 480 \\\B & 9 & 395 \\\C & 2 & 575 \\\D & 8 & 550 \\\E & 5 & 510 \\\F & 1 & 545 \\\G & 7 & 400 \\\H & 4 & 465 \\\I & 3 & 420 \end{array}$$ Is there a significant relationship between the quality and the price of a microwave oven? Use a 0.05 level of significance.

Two judges at a college homecoming parade rank 8 floats in the following order: $$\begin{array}{lccccccccc} & \multicolumn{8}{c} {\text { Float }} \\\\\cline { 2 - 9 } & \multicolumn{1}{c} {1} & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\ \hline \text { Judge } & \text { A } & 5 & 8 & 4 & 3 & 6 & 2 & 7 & 1 \\\\\text { Judge } & \text { B } & 7 & 5 & 4 & 2 & 8 & 1 & 6 & 3\end{array}$$ (a) Calculate the rank correlation. (b) Test the null hypothesis that \(p=0\) against the alternative that \(p>0 .\) Use \(\alpha=0.05 .\)