Problem 3
Noise Levels in Hospitals The mean noise level of 20 randomly selected areas designated as "casualty doors", was \(63.1 \mathrm{dBA}\), and the sample standard deviation is \(4.1 \mathrm{dBA}\). The mean noise level for 24 randomly selected areas designated as operating theaters was \(56.3 \mathrm{dBA}\), and the sample standard deviation was \(7.5 \mathrm{dBA}\). At \(\alpha=0.05,\) can it be concluded that there is a difference in the means?
Problem 3
Find each \(X,\) given \(\hat{p}\) a. \(\hat{p}=0.60, n=240\) b. \(\hat{p}=0.20, n=320\) c. \(\hat{p}=0.60, n=520\) d. \(\hat{p}=0.80, n=50\) e. \(\hat{p}=0.35, n=200\)
Problem 3
For Exercises 2 through \(12,\) perform each of these steps. Assume that all variables are normally or approximately normally distributed. a. State the hypotheses and identify the claim. b. Find the critical value(s). c. Compute the test value. d. Make the decision. e. Summarize the results. Use the traditional method of hypothesis testing unless otherwise specified. Improving Study Habits As an aid for improving students' study habits, nine students were randomly selected to attend a seminar on the importance of education in life. The table shows the number of hours each student studied per week before and after the seminar. At \(\alpha=0.10\), did attending the seminar increase the number of hours the students studied per week? $$ \begin{array}{l|ccccccccc}{\text { Before }} & {9} & {12} & {6} & {15} & {3} & {18} & {10} & {13} & {7} \\ \hline \text { After } & {9} & {17} & {9} & {20} & {2} & {21} & {15} & {22} & {6}\end{array} $$
Problem 4
Find each \(X,\) given \(\hat{p} .\) a. \(\hat{p}=0.24, n=300\) b. \(\hat{p}=0.09, n=200\) c. \(\hat{p}=88 \%, n=500\) d. \(\hat{p}=40 \%, n=480\) e. \(\hat{p}=32 \%, n=700\)
Problem 4
Show two different ways to state that the means of two populations are equal.
Problem 4
What are the characteristics of the \(F\) distribution?
Problem 4
Ages of Gamblers The mean age of a random sample of 25 people who were playing the slot machines is 48.7 years, and the standard deviation is 6.8 years. The mean age of a random sample of 35 people who were playing roulette is 55.3 with a standard deviation of 3.2 years. Can it be concluded at \(\alpha=0.05\) that the mean age of those playing the slot machines is less than those playing roulette?
Problem 4
For Exercises 2 through \(12,\) perform each of these steps. Assume that all variables are normally or approximately normally distributed. a. State the hypotheses and identify the claim. b. Find the critical value(s). c. Compute the test value. d. Make the decision. e. Summarize the results. Use the traditional method of hypothesis testing unless otherwise specified. Obstacle Course Times An obstacle course was set up on a campus, and 8 randomly selected volunteers were given a chance to complete it while they were being timed. They then sampled a new energy drink and were given the opportunity to run the course again. The "before" and "after" times in seconds are shown. Is there sufficient evidence at \(\alpha=0.05\) to conclude that the students did better the second time? Discuss possible reasons for your results. $$ \begin{array}{l|ccccccc}{\text { Student }} & {1} & {2} & {3} & {4} & {5} & {6} & {7} & {8} \\ \hline \text { Before } & {67} & {72} & {80} & {70} & {78} & {82} & {69} & {75} \\ \hline \text { After } & {68} & {70} & {76} & {65} & {75} & {78} & {65} & {68}\end{array} $$
Problem 5
For Exercises 2 through \(12,\) perform each of these steps. Assume that all variables are normally or approximately normally distributed. a. State the hypotheses and identify the claim. b. Find the critical value(s). c. Compute the test value. d. Make the decision. e. Summarize the results. Use the traditional method of hypothesis testing unless otherwise specified. Cholesterol Levels A medical researcher wishes to see if he can lower the cholesterol levels through diet in 6 people by showing a film about the effects of high cholesterol levels. The data are shown. At \(\alpha=0.05,\) did the cholesterol level decrease on average? $$ \begin{array}{lllllll}\hline \text { Patient } & {1} & {2} & {3} & {4} & {5} & {6} \\ \hline \text { Before } & {243} & {216} & {214} & {222} & {206} & {219} \\ \hline \text { After } & {215} & {202} & {198} & {195} & {204} & {213}\end{array} $$
Problem 6
For Exercises 2 through \(12,\) perform each of these steps. Assume that all variables are normally or approximately normally distributed. a. State the hypotheses and identify the claim. b. Find the critical value(s). c. Compute the test value. d. Make the decision. e. Summarize the results. Use the traditional method of hypothesis testing unless otherwise specified. PGA Golf Scores At a recent PGA tournament (the Honda Classic at Palm Beach Gardens, Florida) the following scores were posted for eight randomly selected golfers for two consecutive days. At \(\alpha=0.05\) is there evidence of a difference in mean scores for the two days? $$ \begin{array}{l|cccccccc}{\text { Golfer }} & {1} & {2} & {3} & {4} & {5} & {6} & {7} & {8} \\ \hline \text { Thursday } & {67} & {65} & {68} & {68} & {68} & {70} & {69} & {70} \\ \hline \text { Friday } & {68} & {70} & {69} & {71} & {72} & {69} & {70} & {70}\end{array} $$
