Questions 26 through 29 are based on the following scenario.
A study was conducted to learn whether watching football on television influences color-blindness. A group of subjects was obtained. The responses and results are presented below:
| Watch Football? | |||
| Yes | No | ||
| Color Blind? | Yes | 40 | 10 |
| No | 200 | 110 | |
26.What type of chi-square test should be used to assess if there is a relationship between watching football on television and color-blindness?
27.If there is no relationship between watching football on television and color-blindness, how many subjects would you expect to be color blind and watch football?
28.Compute the appropriate test statistic and report the p-value.
29.State your decision and conclusion using a 5% significance level.
Questions 30 through 34 are based on the following scenario.
A micro-brewery newly opened 2 months ago, is interested to see what kind of beer people prefer. To be able to better advertise these different types of beer, they randomly select 400 women and 500 men and ask what kind of beer they prefer. Their main question of interest is “Are the proportions of the different beer flavors the same for men and women?” The results are given below.
| Light | Regular | Dark | Fruit Flavor | Total | |
| Men | 40 | 190 | 210 | 60 | 500 |
| Women | 65 | 140 | 120 | 75 | 400 |
| Total | 105 | 330 | 330 | 135 | 900 |
30.State the appropriate null hypothesis in terms of the problem.
31.If the null hypothesis were true, how many women would we expect to prefer light beer?
32.What is the value of the test statistic?
33.Are the results statistically significant at the 5% significance level?
34.Explain what your answer to question 33 means in terms of the problem. What would you tell the owner of the micro-brewery?
Questions 35 through 38 are based on the following scenario.
According to USA Today (April 18, 1994) these were the market shares for the different cereal companies:
| Company: | Kellogg | GeneralMills | Post | QuakerOats | Other |
| Share: | 35% | 29% | 12% | 7% | 17% |
A survey of 740 shoppers from grocery stores in California asked for their favorite brand of cereal, and the following data were obtained:
| Company: | Kellogg | GeneralMills | Post | QuakerOats | Other |
| Observed Numberof Preferences: | 220 | 163 | 109 | 95 | 153 |
| Expected Numberof Preferences: | 259 | 214.6 | 88.8 |
We wish to assess if these data support the conjecture that the cereal companies have the same market share in California as nationwide.35. What is the appropriate null hypothesis of interest here?
36.Compute the remaining expected counts and write them in the above table.
37.Compute the appropriate test statistic and report the p-value.
38.State your decision using a 5% significance level and explain what your answer means in terms of the problem.