The general manager of the Cleveland Indians baseball team is in the process of determining which minor-league players to draft. He is aware that his team needs home-run hitters and would like to find a way to predict the number of home runs a player will hit. Being an astute statistician, he gathers a random sample of players and records the number of home runs each player hit in his first two full years as a major-league player, the number of home runs he hit in his last full year in the minor leagues, his age, and the number of years of professional baseball. Test the model’s validity.

The general manager of the Cleveland Indians baseball team is in the process of determining which minor-league players to draft. He is aware that his team needs home-run hitters and would like to find a way to predict the number of home runs a player will hit. Being an astute statistician, he gathers a random sample of players and records the number of home runs each player hit in his first two full years as a major-league player, the number of home runs he hit in his last full year in the minor leagues, his age, and the number of years of professional baseball. Calculate the 95% interval of the number of home runs in the first two years of a player who is 25 years old, has played professional baseball for 7 years, and hit 22 home runs in his last year in the minor leagues.

The general manager of the Cleveland Indians baseball team is in the process of determining which minor-league players to draft. He is aware that his team needs home-run hitters and would like to find a way to predict the number of home runs a player will hit. Being an astute statistician, he gathers a random sample of players and records the number of home runs each player hit in his first two full years as a major-league player, the number of home runs he hit in his last full year in the minor leagues, his age, and the number of years of professional baseball. Calculate the 95% interval of the expected number of home runs in the first two years of players who are 27 years old, have played professional baseball for 5 years, and hit 18 home runs in their last year in the minors.

Perform each of the following steps.

a. State the hypotheses and identify the claim. b. Find the critical value(s). c. Find the test value. d. Make the decision. e. Summarize the results.

Use the traditional method of hypothesis testing unless otherwise specified. An educational researcher devised a wooden toy assembly project to test learning in 6-year-olds. The time in seconds to assemble the project was noted, and the toy was disassembled out of the child's sight. Then the child was given the task to repeat. The researcher would conclude that learning occurred if the mean of the second assembly times was less than the mean of the first assembly times. At $\alpha=0.01$, can it be concluded that learning took place? Use the $P$-value method, and find the $99 \%$ confidence interval of the difference in means.

Perform each of these steps. Assume that all variables are normally or approximately normally distributed.
Use the traditional method of hypothesis testing unless the P-value method is specified by your instructor.
Toy Assembly Test An educational researcher devised a wooden toy assembly project to test learning in $6$- years-olds. The time in seconds to assemble the project was noted. and the toy was disassembled out of the child's sight. Then the child was given the task to repeat. The researcher would conclude that learning occurred if the mean of the second assembly times was less than the mean of the first assembly times. At $\alpha=0.001$,can it be concluded that leaning took place? Use the $P$-value method, and the $99\%$ confidence interval of the difference in means.

$$\begin{array}{l|rrrrrrrr} \text { Child } & 1 & 2 & 3 & 4 & 5 & 6 & 7\\ \hline \text { Trial 1 } & 100 & 150 & 150 & 110 & 130 & 120 & 118 \\ \hline \text { Trial 2 } & 90 & 130 & 150 & 90 & 105 & 110 & 120 &\end{array}$$

d. Make the decision.

Perform each of these steps. Assume that all variables are normally or approximately normally distributed.
Use the traditional method of hypothesis testing unless the P-value method is specified by your instructor.
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 $2$ days?

$$\begin{array}{l|rrrrrrrr} \text { Golfer } & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\ \hline \text { Thursday } & 67 & 65 & 68 & 68 & 68 & 70 & 69 & 70 \\ \hline \text { Friday } & 68 & 70 & 69 & 71 & 72 & 69 & 70 & 70 \end{array}$$

c. Compute the test value.

Perform each of these steps. Assume that all variables are normally or approximately normally distributed.
Use the traditional method of hypothesis testing unless the P-value method is specified by your instructor.
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 $2$ days?

$$\begin{array}{l|rrrrrrrr} \text { Golfer } & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\ \hline \text { Thursday } & 67 & 65 & 68 & 68 & 68 & 70 & 69 & 70 \\ \hline \text { Friday } & 68 & 70 & 69 & 71 & 72 & 69 & 70 & 70 \end{array}$$

e. Summarize the results.

Perform each of these steps. Assume that all variables are normally or approximately normally distributed.
Use the traditional method of hypothesis testing unless the P-value method is specified by your instructor.
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 $2$ days?

$$\begin{array}{l|rrrrrrrr} \text { Golfer } & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\ \hline \text { Thursday } & 67 & 65 & 68 & 68 & 68 & 70 & 69 & 70 \\ \hline \text { Friday } & 68 & 70 & 69 & 71 & 72 & 69 & 70 & 70 \end{array}$$

b. Find the critical value(s) or use the $P$-value method.

Perform each of these steps. Assume that all variables are normally or approximately normally distributed.
Use the traditional method of hypothesis testing unless the P-value method is specified by your instructor.
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 $2$ days?

$$\begin{array}{l|rrrrrrrr} \text { Golfer } & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\ \hline \text { Thursday } & 67 & 65 & 68 & 68 & 68 & 70 & 69 & 70 \\ \hline \text { Friday } & 68 & 70 & 69 & 71 & 72 & 69 & 70 & 70 \end{array}$$

d. Make the decision.

Assume that all variables are normally or approximately normally distributed.
Use the traditional method of hypothesis testing unless the $\mathrm{P}$-value method is specified by your instructor. Assume the variances are unequal.
Miniature Gold Scores A large group of friends went miniature golfing together at a par $54$ course and decided to play on two teams. Arandom sample of scores from each of the two teams is shown. At $\alpha=0.05$, is there a difference in mean scores between the two teams? Use $P$-value method.

$$\begin{array}{c|lllllll} \mathbf{Team 1} & 61 & 44 & 52 & 47 & 56 & 63 & 62 & 55 \\ \hline \mathbf{Team 2} & 56 & 40 & 42 & 58 & 48 & 52 & 51 \end{array}$$

$e$. Summarize the results.

Assume that all variables are normally or approximately normally distributed.
Use the traditional method of hypothesis testing unless the $\mathrm{P}$-value method is specified by your instructor. Assume the variances are unequal.
Home Runs Two random samples of professional baseball players were selected and the number of home runs hit were recorded. One sample was obtained from the National League, and the other sample was obtained from the American League. At $\alpha=0.10$, is there a difference in the means?

$$\begin{array}{r|r} \text { National League } & \text { American League } \\ \hline \ 18 \qquad 4 \qquad 8\qquad 2 & 6 \qquad 11 \qquad 18\qquad 11 \\ 9 \qquad 2 \qquad 6\qquad 5 & 3\qquad 12\qquad 25\qquad 4\\ 6\qquad 8 \ \ \ \quad 29\quad 25 & 24\qquad 9\qquad 12\qquad5 \end{array}$$

a. State the hypotheses and identify the claim.

Let matrix A represent the sales (in thousands of dollars) of a toy company in 2007 in three cities, and let B represent the sales in the same cities in 2009, where

$$A=\begin{array}{c}{\text { Action }} \\ {\text { Educational }}\end{array} \left[\begin{array}{lll}{400} & {350} & {150} \\ {450} & {280} & {850}\end{array}\right] \\ B=\begin{array}{c}{\text { Action }} \\ {\text { Educational }}\end{array} \left[\begin{array}{lll}{380} & {330} & {220} \\ {460} & {320} & {750}\end{array}\right]$$

If the company buys a competitor and doubles its 2009 sales in 2010, what is the change in sales between 2003 and 2010?

Perform each of the following steps.
Use the traditional method of hypothesis testing unless the $\mathrm{P}$-value method is specified by your instructor
Assume that the population is approximately normally distrubuted
Average Family Size The average family size was reported as $3.18.$ A random sample of families in a particular school district resulted in the following family sizes: \

$$\begin{array}{lllllllllll}5 & 4 & 5 & 4 & 4 & 3 & 6 & 4 & 3 & 3 & 5 \\ 6 & 3 & 3 & 2 & 7 & 4 & 5 & 2 & 2 & 2 & 3 \\ 5 & 2 & & & & & & & & & \end{array}$$

At $\alpha=0.05$, does the average family size differ from the national average?
d. Make the decision.

Telephone Calls A researcher knew that before cell phones, a person made on average $2.8$ calls per day. He believes that the number of calls made per day today is higher. He selects a random sample of 30 individuals who use a cell phone and asks them to keep track of the number of calls that they made on a certain day. The mean was $3.1$. At $\alpha=0.01$ is there enough evidence to support the researcher's claim? The standard deviation for the population found by a previous study is $0.8$. Would the null hypothesis be rejected at $\alpha=0.05$ ?
$b$. Find the critical value(s) or use the $P$-value method.