11. A sports researcher is interested in determining if there is a relationship between the number of home team and visiting team wins and different sports. A random sample of 526 games is selected and the results are given below.

	Football	Basketball	Soccer	Baseball
Home Team Wins	40	79	24	45
Visiting Team Wins	35	97	19	76

Determine if the number of home team and visiting team wins are dependent on the sport using a significance level of 0.05.

12. An automotive engineer wanted to determine whether the octane of gasoline used in a car increases gas mileage. He selected six different brands of car and assigned a driver to each car. The miles per gallon was calculated for each car at each level of octane:

	87 Octane	89 Octane	92 Octane
Chev Impala	23.8	28.4	28.7
Chrysler 300M	27.1	26.9	27.2
Ford Taurus	26.4	26.1	26.8
Lincoln LS	26.1	26.4	27.3
Toyota Camry	28.4	28.9	29.1
Volvo	25.3	25.1	25.8

An assistant was in charge of the analysis of this data and was unsure whether one-way or two-way ANOVA should be used, so he performed both. The output is provided below, and you are to use the correct output to answer the questions.

One-way ANOVA: MPG, Brand of Car

Source DF SS MS F P

Factor 1 4918.68 4918.68 1905.36 0.000

Error 34 87.77 2.58

Total 35 5006.46

S = 1.607 R-Sq = 98.25%. R-Sq(adj) = 98.20%

Two-way ANOVA: MPG versus Brand of Car, Octane

Source DF SS MS. F P

Brand of Car 5 18.5911 3.71822 3.22 0.054

Octane 2 5.1411 2.57056 2.23 0.158

Error 10 11.5389 1.15389

Total 17 35.2711

S = 1.074 R-Sq = 67.29% R-Sq(adj) = 44.38%

Is there sufficient evidence at alpha=0.05, that the mean miles per gallon is different among the three octane levels? (for full credit, state the null and alternative hypotheses, p-value, decision AND interpretation)

13. In a survey of 2850 male senior citizens, 1001 said they eat the daily recommended number of servings of vegetables. In a survey of 4150 female senior citizens, 1348 said they eat the daily recommended number of servings of vegetables. At =0.10, does the evidence support the claim that the proportion of senior citizens who said they eat the daily recommended number of servings of vegetables is lower for males than for females?

14. The aluminum bottle is reported to cool faster and stay cold longer than typical glass bottles. A small brewery tests this claim and obtains the following information regarding the time (in minutes) required to chill a bottle of beer from room temperature.

	Clear Glass	Aluminum
Sample Size	42	35
Mean time to chill	133.8	92.4
Sample S.D.	9.9	7.3

a) Is there evidence that the aluminum bottles take less time to cool? (use alpha=0.05 and assume unequal variances)?

b) Is there evidence the time to chill is more variable with the clear glass bottles?

18. A real estate agent claims that there is a difference between the mean household incomes of two neighborhoods. The mean income of 14 randomly selected households from the first neighborhood was 62850 with a standard deviation of 3900. In the second neighborhood, 16 randomly selected households had a mean income of 64200 with a standard deviation of 2825. Assume normal distributions and equal population variances. Test the claim at = 0.10