Prob Set

37.

H0: r ≤ 0

H1: r > 0

α = 0.05

df = N-2 = 25-2 = 23

Critical value = 1.714

Test statistic = r*sqrt[(n-2)/(1-r²)] = 0.94*sqrt[(25-2)/(1-0.94²)] = 13.213

Conclusion: Since 13.213 > 1.714 we reject H0 and conclude that we have sufficient evidence to support claim of a positive association between the two variables.

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We conduct a t- test for a correlation coefficient.

t = [r/sqrt(1 - r^2)] * sqrt(n - 2) = [0.94/sqrt(1 - 0.94^2)] * sqrt(25 - 2) = 13.21

The critical value of t for 23 dof and a = 0.05 is 2.0686

Since 13.21 > 2.0686, we conclude that the correlation between the variables is

significant.

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40.

(A)

(B)

r = 0.423, weak positive correlation.

(C)

df = n-2 = 25-2 = 23

α = 0.05

one-tailed critical value T = 1.319

Test statistic T = r*Sqrt[(n-2)/(1-r²)] = 0.423*Sqrt[(25-2)/(1-0.423²)] = 2.24

Conclusion: Since 2.24 > 1.319 we conclude that there is a positive relationship between the variables.

(D)

r² = 0.423² = 0.179, so approximately 18% of the variation in revenue is explained by the variation in the number of rooms occupied.

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17.

a.     $28,000

b.     R2 = SSR/SS total = 3,050/5,250 = .5809

c.     9.199, found by calculating the sqrt 84.62

d.     Ho is rejected if F > 2.97 (approximately)

Computed F = 1,016.67/84.62 = 12.01

Thus Ho is rejected due to at least one regression coefficient is not zero....