In his book Outliers, author Malcolm Gladwell argues that more American-born baseba]] players have birth dates in the months immediately following July 31 because that was the age cutoff date for nonschool baseball leagues. The table below lists month of births for a sample of American-born basebal l players and foreign-born baseball players. Using a 0.05 significance level, is there sufficient evidence to warrant rejection of the claim that months of births of baseball players are independent of whether they are born in America? Do the data appear to support Gladwell 's claim?

$$\begin{matrix} \text{ } & \text{Jan. } & \text{Feb.} & \text{March} & \text{April} & \text{May} & \text{June} & \text{July} & \text{Aug.} & \text{Sep.} & \text{Oct.} & \text{Nov.} & \text{Dec.}\\ \text{Born in America} & \text{387} & \text{329} & \text{366} & \text{344} & \text{336} & \text{313} & \text{313} & \text{503} & \text{421} & \text{434} & \text{398} & \text{371}\\ \text{Foreign Born} & \text{101} & \text{82} & \text{85} & \text{82} & \text{94} & \text{83} & \text{59} & \text{91} & \text{70} & \text{100} & \text{103} & \text{82}\\ \end{matrix}$$

Members of a certain club are required to register for one of three games: badminton, table tennis or darts. The number of club members of each gender choosing each game in a particular year is shown in the table.

$$\begin{matrix} \text{ } & \text{Badminton} & \text{Table tennis} & \text{Darts}\\ \text{Male} & \text{37} & \text{16} & \text{28}\\ \text{Female} & \text{32} & \text{10} & \text{19}\\ \end{matrix}$$

Use a chi-squared test, at the 5% significance level, to test whether choice of game is independent of gender. State clearly the null and alternative hypotheses, the expected values and the number of degrees of freedom.

The table below lists the numbers of games played in 105 Major League Baseball (MLB) World Series. This table also includes the expected proportions for the numbers of games in a World Series, assuming that in each series, both teams have about the same chance of winning. Use a 0.05 significance level to test the claim that the actual numbers of games fit the distribution indicated by the expected proportions.

$$\begin{array} {|c | c | c | c | c | } \hline \text{Games Played}&4 & { 5 } & { 6 } & { 7 } \\ \hline \text{World Series Contests}&21 & { 23 } & { 23 } & { 38 } \\ \hline \text{Expected Proportion}&2 / 16 & { 4 / 16 } & { 5 / 16 } & { 5 / 16 } \\ \hline \end{array}$$

The author drilled a hole in a die and filled it with a lead weight, then proceeded to roll it 200 times. Here are the observed frequencies for the outcomes of 1, 2, 3, 4, 5, and 6, re pectively: 27, 31, 42, 40, 28, and 32. Use a 0.05 significance level to test the claim that the outcomes are not equally likely. Does it appear that the loaded die behaves differently than a fair die?

In soccer, serious fouls in the penalty box result in a penalty kick with one kicker and one defending goalkeeper. The table below summarizes results from 286 kicks during games among top teams (based on data from "Action Bias Among Elite Soccer Goalkeepers: The Case of Penalty Kicks," by Bar-Eli et al. , Journal of Economic Psychology, Vol. 28, No. 5). In the table, jump direction indicates which way the goalkeeper jumped, where the kick direction is from the perspective of the goalkeeper. Use a 0.05 significance level to test the claim that the direction of the kick is independent of the direction of the goalkeeper jump. Do the results support the theory that because the kicks are so fast, goalkeepers have no time to react, so the directions of their jumps are independent of the directions of the kicks? Goalkeeper Jump

$$\begin{matrix} \text{ } & \text{Left} & \text{Center} & \text{Right}\\ \text{Kick to Left} & \text{54} & \text{1} & \text{37}\\ \text{Kick to Center} & \text{41} & \text{10} & \text{31}\\ \text{Kick to Right} & \text{46} & \text{7} & \text{59}\\ \end{matrix}$$

Jose started at his home, H(0, 0) and walked to a park located at P(4, 2). He then went to Jacintha's house located at F(8, 0). Later, he walked straight home. If each unit on the coordinate plane represents 50 feet, what is the distance that Jose walked, to the nearest foot?

Identify the null hypothesis, alternative hypothesis, test statistic, P-value or critical value(s), then state the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim. In a study of treatments for very painful "cluster" headaches, 150 patients were treated with oxygen and 148 other patients were given a placebo consisting of ordinary air. Among the 150 patients in the oxygen treatment group, 116 were free from headaches 15 minutes after treatment. Among the 148 patients given the placebo, 29 were free from headaches 15 minutes after treatment (based on data from "High-Flow Oxygen for Treatment of Cluster Headache," by Cohen, Burns, and Goadsby, Journal of the American Medical Association, Vol. 302, No. 22). We want to use a 0.01 significance level to test the claim that the oxygen treatment is effective. Test the claim using a hypothesis test.

Children Researchers conducted a study to assess the effects that occur when children are exposed to cocaine before birth. Children were tested at age 4 for object assembly skill, which was described as "a task requiring visual-spatial skills related to mathematical competence." The 190 children born to cocaine users had a mean of $7.3$ and a standard deviation of 3.0. The 186 children not exposed to cocaine had a mean score of $8.2$ with a standard deviation of 3.0. (The data are based on "Cognitive Outcomes of Preschool Children with Prenatal Cocaine Exposure," by Singer, et al., Journal of the American Medical Association, Vol. 291, No. 20.) Use a $0.05$ significance level to test the claim that prenatal cocaine exposure is associated with lower scores of four-year-old children on the test of object assembly.

The table below includes results from polygraph (lie detector) experiments conducted by researchers Charles R. Honts (Boise State University) and Gordon H. Barland (Department of Defense Polygraph Institute). In each case, it was known if the subject lied or did not lie, so the table indicates when the polygraph test was correct. Use a 0.05 significance level to test the claim that whether a subject lies is independent of the polygraph test indication. Do the results suggest that polygraphs are effective in distinguishing between truths and lies?

$$\begin{matrix} \text{ } & \text{Did the Subject } & \text{Actually Lie?}\\ & \text{No (Did not Lie)} & \text{Yes (Lied)}\\ \text{Polygraph test indicated that the subject lied.} & \text{15} & \text{42}\\ \text{Polygraph test indicated that the subject did not lie.} & \text{32} & \text{9}\\ \end{matrix}$$

Listed below are amounts of strontium-90 (in millibecquerels, or mBq, per gram of calcium) in a simple random sample of baby teeth obtained from Pennsylvania residents and New York residents born after 1979 (based on data from "An Unexpected Rise in Strontium-90 in U.S. Deciduous Teeth in the 1990s," by Mangano et al., Science of the Total Environment). Use a 0.05 significance level to test the claim that the median amount of strontium-90 from Pennsylvania residents is the same as the median from New York residents.

$$\begin{array} {|c | c | c | c | c | c | c | c | c | } \hline \text{Pennsylvania}&155 & { 142 } & { 149 } & { 130 } & { 151 } & { 163 } & { 151 } & { 142 } & { 156 } & { 133 } & { 138 } & { 161 } \\ \hline \text{New York}&133 & { 140 } & { 142 } & { 131 } & { 134 } & { 129 } & { 128 } & { 140 } & { 140 } & { 140 } & { 137 } & { 143 } \\ \hline \end{array}$$

a. Write a brief definition for each of the following terms: county and sheriff. b. Describe the organization of county government c. What are some of the duties of county government?

In a carbonated beverage, the main ingredients are water and carbon dioxide. Carbon dioxide gas is released when the bottle is opened. Why is water a liquid but carbon dioxide a gas at room temperature?

A classic story involves four carpooling students who missed a test and gave as an excuse a flat tire. On the makeup test, the instructor asked the students to identify the particular tire that went flat. If they really didn't have a flat tire, would they be able to identify the same tire? The author asked 41 other students to identify the tire they would select. The results are listed in the following table (except for one student who selected the spare). Use a 0.05 significance level to test the author's claim that the results fit a uniform distribution. What does the result suggest about the likelihood of four students identifying the ame tire when they really didn 't have a flat?

$$\begin{array} { |c|c | c |c |c| }\text{Tire}& { \text { Left Front } } & { \text { Right Front } } & { \text { Left Rear } } & { \text { Right Rear } } \\ \text{Number selected}&{ 11 } & { 15 } & { 8 } & { 6 } \end{array}$$

a. Write a brief definition for the terms birthrate and death rate. b. What are three ways in which a country may grow in population?