Problem 3
What are the two different degrees of freedom associated with the \(F\) distribution?
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
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
What are the characteristics of the \(F\) distribution?
Problem 4
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. $$ \begin{array}{l|rrrrrrrr} \text { Student } & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\ \hline \text { Before } & 67 & 72 & 80 & 70 & 78 & 82 & 69 & 75 \\ \hline \text { After } & 68 & 70 & 76 & 65 & 75 & 78 & 65 & 68 \end{array} $$
Problem 4
Show two different ways to state that the means of two populations are equal.
Problem 5
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? $$ \begin{array}{lrrrrrr} \text { Patient } & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline \text { Before } & 243 & 216 & 214 & 222 & 206 & 219 \\ \hline \text { After } & 215 & 202 & 198 & 195 & 204 & 213 \end{array} $$
Problem 5
Find \(\hat{p}\) and \(\hat{q}\) for each. a. \(X_{1}=25, n_{1}=75, X_{2}=40, n_{2}=90\) b. \(X_{1}=9, n_{1}=15, X_{2}=7, n_{2}=20\) c. \(X_{1}=3, n_{1}=20, X_{2}=5, n_{2}=40\) d. \(X_{1}=21, n_{1}=50, X_{2}=32, n_{2}=50\) e. \(X_{1}=20, n_{1}=150, X_{2}=30, n_{2}=50\)
Problem 5
The number of grams of carbohydrates contained in 1 -ounce servings of randomly selected chocolate and nonchocolate candy is listed here. Is there sufficient evidence to conclude that the difference in the means is statistically significant? Use \(\alpha=0.10\) $$ \begin{array}{lllllllll}\text { Chocolate: } & 29 & 25 & 17 & 36 & 41 & 25 & 32 & 29 \\\& 38 & 34 & 24 & 27 & 29 & & & \\\\\text { Nonchocolate: } & 41 & 41 & 37 & 29 & 30 & 38 & 39 & 10 \\ & 29 & 55 & 29 & & & & &\end{array}$$
Problem 5
Perform each of the following steps. 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. A researcher wishes to see if there is a difference between the mean number of hours per week that a family with no children participates in recreational activities and a family with children participates in recreational activities. She selects two random samples and the data are shown. At \(\alpha=0.10\), is there a difference between the means? $$ \begin{array}{lrcl} & \bar{X} & \sigma & n \\ \hline \text { No children } & 8.6 & 2.1 & 36 \\ \text { Children } & 10.6 & 2.7 & 36 \end{array} $$
