Problem 3 A bowl contains 12 balls of various colors: color silver magenta umber copper balls in bowl 2 3 1 6 Consider drawing a random sample of size 6 with replacement from the bowl. Fill in the following table of expected values of the numbers of balls of each color in the random sample. color expected number (03) silver Fill in the expected values magenta (Q5) umber (Q6) color silver magenta umber copper balls in sample 1 2 1 2 copper (Q4) Consider the following possible outcome of drawing the random sample: The probability of this outcome is (Q7) The chi-squared statistic for this outcome is (Q8) Is the chi-square curve with 3 degrees of freedom a good approximation to the probability histogram of the chi-squared statistic for a random sample of size 6

6. A simple random sample of 1,000 United States adults was collected to investigate whether gender and being a coffee drinker are independent. The results are summarized in the table with the expected counts shown in parentheses. Coffee Drinker? Yes No Total Male 191 (148.5) 299 (341.5) 490 Gender Female 112 (154.5) 398 (355.5) 510 Total 303 697 1,000 Which statement is true about whether the conditions for the chi-square test for independence have been met? All necessary conditions are satisfied to apply a chi-square test for independence between gender and being a coffee drinker. The data is not the result of two independent random samples; therefore, the conditions for applying the chi- square test for independence between gender and being a coffee drinker are not met. Not all of the expected cell counts are large enough to satisfy the conditions for applying the chi-square test (c) for independence between gender and being a coffee drinker. Not all of the observed cell counts are…

Rock-paper-scissors is a game played by two or more people where players choose either rock, paper, or scissors with their hands. For your statistics class project, you want to evaluate whether players choose between these three options randomly, or if certain options are favored above others. You ask two friends to play rock-paper-scissors and count the times each option is played. The following table summarizes the data:   Under the assumption that no option is favored, what would the expected number of paper be?    a. 33   b. 20   c. Impossible to determine   d. 21   e. 0.33 What is the test statistic for the chi-square goodness of fit test?   a. 0.0005   b. 0   c. 0.30   d. 0.317   e. 0.20   f. 7.51

Are birthdays "evenly distributed" throughout the year, or are they more common during some parts of the year than others? Owners of a children's toy store chain in the Northwest asked just this question. Some data collected by the chain are summarized in the table below. The data were obtained from a random sample of 190 people. The birthdate of each person was recorded, and each of these dates was placed into one of four categories: winter (December 21-March 20), spring (March 21-June 20), summer (June 21-September 20), and fall (September 21-December 20). The numbers in the first row of the table are the frequencies observed in the sample for these season categories. The numbers in the second row are the expected frequencies under the assumption that birthdays are equally likely during each season of the year. The bottom row of numbers gives the following value for each of the season categories. Answer the following to summarize the test of the hypothesis that birthdays are equally…