In a tennis match, unforced errors are those types of mistakes that are supposedly not forced by good shots of an opponent. Reducing unforced errors is a key factor to win a tennis match. The following table shows the number of unforced errors of both players (winner and loser reported in pairs) in 10 tennis matches. Match: 1 3 4 6. 7 8. 9. 10 Winner: 68 19 28 28 53 28 50 30 44 22 Loser: 52 39 32 22 75 51 51 37 37 34 N (ux,o) be the average number of unforced errors of the winner in a tennis match, - N(µy,o) be the average number of unforced errors of the loser in a tennis match. Let X and Y Some R output that may help. > р1 <- с(0.01, 0.025, 0.05, 0.1, 0.9, 0.95, 0.975, 0.99) > qnorm(p1) [1] -2.326 -1.960 -1.645 -1.282 1.282 1.645 1.960 2.326 > qt (p1, 8) [1] -2.896 -2.306 -1.860 -1.397 1.397 1.860 2.306 2.896 > qt (p1, 9) [1] -2.821 -2.262 -1.833 -1.383 > qt (p1, 18) 1.383 1.833 2.262 2.821 [1] -2.552 -2.101 -1.734 -1.330 1.330 1.734 2.101 2.552 > qt (p1, 19) [1] -2.539 -2.093 -1.729 -1.328 1.328 1.729 2.093 2.539

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A) Construct a two-sided 95% confidence interval for µY . 

B) Test H0 : µX = µY versus H1 : µX < µY with significance level α = 0.05.

In a tennis match, unforced errors are those types of mistakes that are supposedly not forced by
good shots of an opponent. Reducing unforced errors is a key factor to win a tennis match. The
following table shows the number of unforced errors of both players (winner and loser reported
in pairs) in 10 tennis matches.
Match:
1
3
4
6.
7
8.
9.
10
Winner:
68
19
28
28
53
28
50
30
44
22
Loser:
52
39
32
22
75
51
51
37
37
34
N (ux,o) be the average number of unforced errors of the winner in a tennis match,
- N(µy,o) be the average number of unforced errors of the loser in a tennis match.
Let X
and Y
Some R output that may help.
> р1 <- с(0.01, 0.025, 0.05, 0.1, 0.9, 0.95, 0.975, 0.99)
> qnorm(p1)
[1] -2.326 -1.960 -1.645 -1.282
1.282
1.645
1.960
2.326
> qt (p1, 8)
[1] -2.896 -2.306 -1.860 -1.397
1.397
1.860
2.306
2.896
> qt (p1, 9)
[1] -2.821 -2.262 -1.833 -1.383
> qt (p1, 18)
1.383
1.833
2.262
2.821
[1] -2.552 -2.101 -1.734 -1.330
1.330
1.734
2.101
2.552
> qt (p1, 19)
[1] -2.539 -2.093 -1.729 -1.328
1.328
1.729
2.093
2.539
Transcribed Image Text:In a tennis match, unforced errors are those types of mistakes that are supposedly not forced by good shots of an opponent. Reducing unforced errors is a key factor to win a tennis match. The following table shows the number of unforced errors of both players (winner and loser reported in pairs) in 10 tennis matches. Match: 1 3 4 6. 7 8. 9. 10 Winner: 68 19 28 28 53 28 50 30 44 22 Loser: 52 39 32 22 75 51 51 37 37 34 N (ux,o) be the average number of unforced errors of the winner in a tennis match, - N(µy,o) be the average number of unforced errors of the loser in a tennis match. Let X and Y Some R output that may help. > р1 <- с(0.01, 0.025, 0.05, 0.1, 0.9, 0.95, 0.975, 0.99) > qnorm(p1) [1] -2.326 -1.960 -1.645 -1.282 1.282 1.645 1.960 2.326 > qt (p1, 8) [1] -2.896 -2.306 -1.860 -1.397 1.397 1.860 2.306 2.896 > qt (p1, 9) [1] -2.821 -2.262 -1.833 -1.383 > qt (p1, 18) 1.383 1.833 2.262 2.821 [1] -2.552 -2.101 -1.734 -1.330 1.330 1.734 2.101 2.552 > qt (p1, 19) [1] -2.539 -2.093 -1.729 -1.328 1.328 1.729 2.093 2.539
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