Data on 19 randomly selected athletes was obtained concerning their cardiovascul
ID: 3224955 • Letter: D
Question
Data on 19 randomly selected athletes was obtained concerning their cardiovascular fitness (measured by time to exhaustion running on a treadmill) and performance in a 20-km ski race. Both variables were measured in minutes and a regression analysis was performed. Ski = 85 - 2.3 * Treadmill Is there sufficient evidence to conclude that there is a linear relationship between cardiovascular fitness and ski race performance? The test statistic is The p-value is between and The local utility company surveys 12 randomly selected customers. For each survey participant, the company collects the following: annual electric bill (in dollars) and home size (in square feet). Output from a regression analysis appears below: Bill = 11 + 3.6*Size We are 99% confident that the mean annual electric bill increases by between dollars and dollars for every additional square foot in home size.Explanation / Answer
1.) Ski = 85 - 2.3*treadmill
b1 = -2.3; SE = 1.06
t = b1 / SE = -2.3/1.06 = -2.169
Test Statistic = -2.169
Now, DF = n - 2 = 19 - 2 = 17
From t-distribution calculator we can say that the P-value ==> -0.0223 p 0.0223
2.) Bill = 11 + 3.6*Size
b1 = 3.6; SE = 0.83
DF = 12 - 2 = 10
Critical Probability at 99% confidence = 2.764
Margin of Error (ME) = 2.764*0.83 = 2.294
CI = (3.6 ± 2.294)
= (1.305, 5.894)
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