# Directions: Be sure to save an electronic copy

Directions: Be sure to save an electronic copy of your answer before submitting it to Ashworth College for grading. Unless otherwise stated, answer in complete sentences, and be sure to use correct English, spelling, and grammar. Refer to the “Assignment Format” page located on the Course Home Page for specific format requirements. NOTE: Show your work in the problems. 1. In families with four children, you’re interested in the probabilities for the different possible numbers of girls in a family. Using theoretical probability (assume girls and boys are equally likely), compile a five-column table with the headings “0” through “4,” for the five possible numbers of girl children in a four-child family. Then, using “G” for girls and “B” for boys, list under each heading the various birth-order ways of achieving that number of girls in a family. Then, use your table to calculate the following probabilities: a. The probability of 1 girl b. The probability of 2 girls c. The probability of 4 girls d. The probability the third child born is a girl 2. As pictured in Figure 6.11 of your textbook, a roulette wheel has 38 numbers: 18 odd black numbers from 1 to 35, 18 even red numbers from 2 to 36, and the two green numbers 0 and 00. Using theoretical probability, calculate the following: a. The probability of spinning a green number b. The probability of spinning a number greater than 30 c. The probability of spinning a red number less than 10 d. The probability of spinning an even black number e. The expected total of green numbers in 57,000 spins 3. In a nationwide polls of 1,500 randomly selected U.S. residents, 77% said that they liked pizza. In a poll of 1,500 randomly selected U.S. residents one month later, 75% responded that they liked pizza. a. Does the polling evidence support the claim that pizza declined in popularity over the month between polls? Explain why or why not. b. Using statistical terminology, precisely identify the population parameter the two polls were attempting to measure. How does a parameter differ from a statistic? c. Based on the two polls, what would you say to someone who guessed that the population parameter the polls are trying to measure is really only 50%? 4. Eleven people have eleven different favorite numbers from 2 to 12. They all agree to participate in a 10,000-roll dice game where they bet $1 on their favorite number for each roll of two standard (fair) dice. A donor kicks in an extra dollar every round, so the payoff if your number comes up is $12. a. Assuming everyone bets on all 10,000 rounds, what is the expected value for a person who has number 7? (Show your calculations.) b. Assuming everyone bets on all 10,000 rounds, what is the expected value for a person who has number 2? (Show your calculations.) Directions: Be sure to save an electronic copy of your answer before submitting it to Ashworth College for grading. Unless otherwise stated, answer in complete sentences, and be sure to use correct English, spelling, and grammar. Refer to the “Assignment Format” page located on the Course Home Page for specific format requirements. NOTE: Show your work in the problems. 1. In the following situations, indicate whether you’d use the normal distribution, the t distribution, or neither. a. The population is normally distributed, and you know the population standard deviation. b. You don’t know the population standard deviation, and the sample size is 35. c. The sample size is 22, and the population is normally distributed. d. The sample size is 12, and the population is not normally distributed. e. The sample size is 45, and you know the population standard deviation. 2. The prices of used books at a large college bookstore are normally distributed. If a sample of 23 used books from this store has a mean price of $27.50 with a standard deviation of $6.75, use Table 10.1 in your textbook to calculate the following for a 95% confidence level about the population mean. Be sure to show your work. a. Degrees of freedom b. The critical value of t c. The margin of error d. The confidence interval for a 95% confidence level 3. Statistics students at a state college compiled the following two-way table from a sample of randomly selected students at their college: Male students Female students Play chess Don’t play chess 25 162 19 148 Answer the following questions about the table. Be sure to show any calculations. a. How many students in total were surveyed? b. How many of the students surveyed play chess? c. What question about the population of students at the state college would this table attempt to answer? d. State Hº and Hª for the test related to this table. 4. Answer the following questions about an ANOVA analysis involving three samples. a. In this ANOVA analysis, what are we trying to determine about the three populations they’re taken from? b. State the null and alternate hypotheses for a three-sample ANOVA analysis. c. What sample statistics must be known to conduct an ANOVA analysis? d. In an ANOVA test, what does an F test statistic lower than its critical value tell us about the three populations we’re examining? …

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