Hockey's Highest Scorers The number of points held by a sample of the NHL's highest scorers for both the Eastern Conference and the Western Conference is shown below. At a=0.10, can it be concluded that there is a difference in means based on these data? Assume the variables are normally distributed and the variances are unequal. Eastern Conference Western Conference 61 89 62 88 77 64 72 66 83 59 60 98 59 58 37 57 75 78 70 62 66 55 61 64 61 59 62 66 Send data to Excel Use u, for the mean score for the Eastern Conference. Part: 0 / 5 Part 1 of 5 State the hypotheses and identify the claim with the correct hypothesis. Ho : |(Choose one) ▼ H : (Choose one) ▼ This hypothesis test is a(Choose one) ▼ test.

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Hockey's Highest Scorers The number of points held by a sample of the NHL's highest scorers for both the Eastern Conference and the Western Conference is shown below. At
a = 0.01, can it be concluded that there is a difference in means based on these data? Assume the variables are normally distributed and the variances are unequal.
Eastern Conference Western Conference
77 37 72 57
75 78 70
88
62 59 61 98
66
55
61
64
59
62
70 71
66
68
76
82
Send data to Excel
Use u, for the mean score for the Eastern Conference.
(a) State the hypotheses and identify the claim with the correct hypothesis.
(b) Find the critical value(s).
(c) Compute the test value.
(d) Make the decision.
(e) Summarize the results.
Explanation
(a) State the hypotheses and identify the claim with the correct hypothesis.
The null hypothesis IH, is the statement that there is no difference between the means. This is equivalent to u, -H,.
The alternative hypothesis H is the statement that there is a difference between the means. This is equivalent to u, #µ,.
The problem asks if "there is a difference in means based on these data." Hence, the claim is the alternative hypothesis H,.
(b) Find the critical value(s).
For this problem, n, = 13 and n, = 11. The degrees of freedom are the smaller of 13 –1= 12 or 11-1= 10. Hence, d.f. = 10.
From OThe t Distribution Table, for a two-tailed test with a = 0.01 and d.f. = 10, the critical values are 13.169.
(c) Compute the test value.
Use a calculator/computer/formulas in Chapter 3 to compute the sample statistics for each conference. The results are shown below (Round the sample means and standard deviations
to two decimal places):
Eastern Conference Western Conference
Sample mean
71.92
63.55
Sample standard deviation
12.06
11.25
Sample size
13
11
Using the formula for the i test-for testing the difference between two means-independent samples, compute the test value:
(X, - X2)- (H, – 4-)
2.
-+-
(71.92 – 63.55)-0
12.06 11.25?
13
11
= 1.757
Hence, the test value rounded to three decimal places is t= 1.757.
(d) Make the decision.
Since the test value does not fall in the critical region, do not reject the null hypothesis.
Transcribed Image Text:Sample Question Hockey's Highest Scorers The number of points held by a sample of the NHL's highest scorers for both the Eastern Conference and the Western Conference is shown below. At a = 0.01, can it be concluded that there is a difference in means based on these data? Assume the variables are normally distributed and the variances are unequal. Eastern Conference Western Conference 77 37 72 57 75 78 70 88 62 59 61 98 66 55 61 64 59 62 70 71 66 68 76 82 Send data to Excel Use u, for the mean score for the Eastern Conference. (a) State the hypotheses and identify the claim with the correct hypothesis. (b) Find the critical value(s). (c) Compute the test value. (d) Make the decision. (e) Summarize the results. Explanation (a) State the hypotheses and identify the claim with the correct hypothesis. The null hypothesis IH, is the statement that there is no difference between the means. This is equivalent to u, -H,. The alternative hypothesis H is the statement that there is a difference between the means. This is equivalent to u, #µ,. The problem asks if "there is a difference in means based on these data." Hence, the claim is the alternative hypothesis H,. (b) Find the critical value(s). For this problem, n, = 13 and n, = 11. The degrees of freedom are the smaller of 13 –1= 12 or 11-1= 10. Hence, d.f. = 10. From OThe t Distribution Table, for a two-tailed test with a = 0.01 and d.f. = 10, the critical values are 13.169. (c) Compute the test value. Use a calculator/computer/formulas in Chapter 3 to compute the sample statistics for each conference. The results are shown below (Round the sample means and standard deviations to two decimal places): Eastern Conference Western Conference Sample mean 71.92 63.55 Sample standard deviation 12.06 11.25 Sample size 13 11 Using the formula for the i test-for testing the difference between two means-independent samples, compute the test value: (X, - X2)- (H, – 4-) 2. -+- (71.92 – 63.55)-0 12.06 11.25? 13 11 = 1.757 Hence, the test value rounded to three decimal places is t= 1.757. (d) Make the decision. Since the test value does not fall in the critical region, do not reject the null hypothesis.
Hockey's Highest Scorers The number of points held by a sample of the NHL's highest scorers for both the
Eastern Conference and the Western Conference is shown below. At a=0.10, can it be concluded that there is a
difference in means based on these data? Assume the variables are normally distributed and the variances are
unequal.
Eastern Conference
Western Conference
61
89
62
88
77
64
72
66
83
59
60
98
59
58
37
57
75
78
70
62
66
55
61
64
61
59
62
66
Send data to Excel
Use u, for the mean score for the Eastern Conference.
Part: 0 / 5
Part 1 of 5
State the hypotheses and identify the claim with the correct hypothesis.
Ho :
|(Choose one) ▼
H :
(Choose one)
This hypothesis test is a(Choose one) ▼
test.
Transcribed Image Text:Hockey's Highest Scorers The number of points held by a sample of the NHL's highest scorers for both the Eastern Conference and the Western Conference is shown below. At a=0.10, can it be concluded that there is a difference in means based on these data? Assume the variables are normally distributed and the variances are unequal. Eastern Conference Western Conference 61 89 62 88 77 64 72 66 83 59 60 98 59 58 37 57 75 78 70 62 66 55 61 64 61 59 62 66 Send data to Excel Use u, for the mean score for the Eastern Conference. Part: 0 / 5 Part 1 of 5 State the hypotheses and identify the claim with the correct hypothesis. Ho : |(Choose one) ▼ H : (Choose one) This hypothesis test is a(Choose one) ▼ test.
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