The data below shows the high temperatures and the times (in minutes) runners wh

Question

The data below shows the high temperatures and the times (in minutes) runners who won a marathon. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the P-value using alpha = 0.05. Is there sufficient evidence to conclude that there is a linear correlation between temperature and winning times The linear correlation coefficient is The test statistic t is The P-value is sufficient evidence to support the claim that there is a linear correlation between between temperature and winning times for a significance level of a = 0.05. Does it appear that winning times are affected by temperature No, because there is a linear correlation between the two variables. Yes, because there is not a linear correlation between the two variables. No, because there is not a linear correlation between the two variables. Yes, because there is a linear correlation between the two variables.

Explanation / Answer

Using technology, we get the correlation,              
              
r =    -0.207270986   [ANSWER]

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Here, n = 8. Hence, as t = r sqrt [(n - 2) / (1 - r^2)], then              
              
t =    -0.518978516   [ANSWER, TEST STATISTIC]

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As
  
df = n - 2 =   6          
              
Then for a two tailed test, the P value is, using technology,

Pvalue = 0.622354222 [ANSWER]

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Because the P value is GREATER THAN the significance level of 0.05, there IS NO SUFFICIENT EVIDENCE... [ANSWER]

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From the previous part,

OPTION C: No, there is not a linear correlation between the two variables. [ANSWER, C]

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