For t-tests and ANOVA, provide the following: S tate the null and alternative hypotheses Verify that assumptions

For t-tests and ANOVA, provide the following:

S tate the null and alternative hypotheses
Verify that assumptions are met
Calculate the test statistic
Calculate the p-value
State the conclusion
For Chi-square tests, provide the following:
S tate the null and alternative hypotheses
Calculate expected values.
Calculate the p-value
State the conclusion

A sports writer wanted to see if a football filled with helium travels further when kicked, on average, than a football filled with air. To test this, the writer used 40 adult male volunteers. These volunteers were randomly divided into two groups of 20 subjects each. Group 1 kicked a football filled with helium to the recommended pressure. Group 2 kicked a football filled with air to the recommended pressure. The mean yardage of each kick is provided in the table below. Assume the two groups of kicks are independent and normality of the populations. Is there sufficient evidence that the mean distance travelled for a football filled with helium is longer than the mean distance travelled for a football filled with air at the α=.05 significance level?

Group 1-Helium	Group 2-Air
30	32
24	27
23	21
32	19
45	24
27	30
34	26
22	35
28	15
36	21
43	33
26	31
33	23
42	28
19	16
28	24
24	29
38	28
32	30
20	18

2. A tool manufacturer tests three types of cutters used in a lathe operation. One type is a laminated steel cutter consisting of very hard high carbon steel sandwiched between two softer steels. Another is a special high speed tool steel cutter developed using powder metallurgy. The final one is made from cryogenically treated steel. Several cutters of each type are tested to see how long they will last (in hours) in continuous operation until they need to be sharpened. The times are recorded for each cutter used in the study and the results are summarized below. Assume the data are three independent simple random samples, one from each of the three populations of cutters, and the distribution of the times until sharpening is needed is normal. Is there sufficient evidence that there is a difference in the mean time until sharpening between the three cutters at the α=.05 significance level?

laminated steel	high-speed steel	cryogenically treated steel
24.99	40.36	45.67
27.46	26.47	40.78
30.68	39.95	28.11
33.67	26.28	47.88
28.26	48.54	38.77
40.55	32.40	28.77
28.17	26.11	36.85
31.47	44.14	41.80
45.11	31.35	50.16
45.82	36.11	36.18
30.97	36.77	30.51
21.90	32.67	38.76
43.00	28.28	37.59
49.44	48.17	32.95
36.69	29.37	32.97
37.64	34.34	42.17
38.00	37.76	29.98
29.36	16.06	51.76
39.00	20.41	20.49
45.86	46.31	43.57
42.61	24.34	37.96
42.23	21.97	44.20
39.60	40.98	45.12
37.86	23.67	42.25
28.74	35.36	38.15
35.81	28.00	38.45
37.02	26.27	41.05
41.57		40.23
30.94		39.07
37.70		26.73
33.00		41.01
18.25		35.69
		36.06
		31.02
		40.01
		22.62
		36.13
		16.89
		34.71

3. Twelve runners are asked to run a 10-kilometer race on each of two consecutive weeks. In one of the races the runners wear one brand of shoe and in the other a second brand. The brand they wear in each race is determined at random. All runners are timed and are asked to run their best in each race. The results in minutes are given below. Assume normality of the populations. Is there sufficient evidence that the mean time using brand 1 is different than the mean times using brand 2?

Runner	Brand 1	Brand 2
1	31.23	32.02
2	29.33	28.98
3	30.50	30.63
4	32.20	32.67
5	33.08	32.95
6	31.52	31.53
7	30.68	30.83
8	31.05	31.10
9	33.00	33.12
10	29.67	29.50
11	30.55	30.57
12	32.12	32.30

4. An old saying in golf is "You drive for the show and putt for the dough." The thought is that good putting is more important than long driving for shooting low scores and hence winning money. To see if this is the case, data on the top 25 money winners on the PGA tour in 2013 were examined. Use the data below to determine whether or not the 2013 putting totals has an effect on the total winnings.

a. Calculate the correlation coefficient and determine whether this relationship is significant using the appropriate statistical test.

b. Provide a scatterplot of 2013 Total Winnings by 2013 Putting Totals. Show the trendline and least-squares regression equation on the plot.

c. Determine whether linear regression is an appropriate method to assess this relationship and analyze the fit of your regression equation to the data.

d. If appropriate, use the least squares regression equation to predict the total winnings for a golfer with a putting total of 175.

e. If appropriate, use the least squares regression equation to predict the total winnings for a golfer with a putting total of 400.

Rank	Golfer	2013 Putting Totals	2013 Total Winnings
1	Tiger Woods	85.3	8,553,439
2	Henrik Stenson	199.8	6,388,230
3	Matt Kuchar	103.8	5,616,808
4	Phil Mickelson	84	5,495,793
5	Brandt Snedeker	107.8	5,318,087
6	Adam Scott	169.8	4,892,611
7	Steve Stricker	82.8	4,440,532
8	Justin Rose	202.6	4,146,148
9	Zach Johnson	184.5	4,044,509
10	Jordan Spieth	195.3	3,879,820
11	Keegan Bradley	146.8	3,636,813
12	Jason Day	156	3,625,030
13	Billy Horschel	69.8	3,501,703
14	Bill Haas	189.3	3,475,563
15	Jim Furyk	173.4	3,204,779
16	Jason Dufner	262.3	3,132,268
17	Kevin Streelman	109.8	3,088,284
18	Hunter Mahan	111.4	3,036,164
19	Dustin Johnson	248.3	2,963,214
20	Webb Simpson	130.4	2,957,582
21	Graham DeLaet	173	2,834,900
22	Boo Weekley	336.5	2,786,662
23	D.A. Points	240.4	2,658,887
24	Nick Watney	210.7	2,477,639
25	Charl Schwartzel	100.5	2,256,723

Sources:

Total Winnings: http://www.pgatour.com/stats/stat.109.html#2013

Putting Totals: http://www.pgatour.com/stats/stat.02428.html#2013

5. (20 points) When a police officer responds to a call for help in a case of spousal abuse, what should the officer do? A randomized controlled experiment in Charlotte, North Carolina studied three police responses to spousal abuse: advise and possibly separate the couple, issue a citation to the offender, and arrest the offender. The effectiveness of the three responses was determined by re-arrest rates. The following table shows these rates.

Number of subsequent arrests	Arrests	Citation	Advise/Separate
0	175	181	187
1	54	33	34
2	17	7	18
3	16	6	12
4	10	8	6

Is there sufficient evidence that there is an association between police responses to spousal abuse and number of subsequent arrests? (Hint: test the null hypothesis that the proportion of subsequent arrests is the same regardless of the treatment assigned.)

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Solution: The downloadable solution consists of 21 pages, 1489 words and 5 charts.
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