On May 25, 2010, LiveScience published an article titled "Simple Memory Test Predicts Intelligence." The article summarized a study that found that the score on a test of working memory capacity was correlated with a number of different measures of intelligence. One measure was cognitive functioning score. Suppose that one such linear regression for working memory capacity and cognitive functioning score from a sample of 12 people is  ŷ = 6.2 + 26.7x,  where y is the cognitive functioning score and x is the working memory score. (a) In a hypothesis test for the slope of the linear regression, which of the following would be the correct alternative hypothesis? Ha: ? = 0 Ha: ? > 26.7      Ha: ? ≠ 0 Ha: ? < 26.7 (b) Given the standard error of the slope, 5.2, calculate the test statistic. (Round your answer to four decimal places.)   (c) Calculate the P-value and determine which conclusion is correct for the hypothesis test based on  ? = 0.05.  (Use technology.) We would reject the null hypothesis. There is insufficient evidence of a linear relationship between working memory capacity and cognitive functioning score.We would fail to reject the null hypothesis. There is insufficient evidence of a linear relationship between working memory capacity and cognitive functioning score.    We would reject the null hypothesis. There is sufficient evidence of a linear relationship between working memory capacity and cognitive functioning score.We would fail to reject the null hypothesis. There is sufficient evidence of a linear relationship between working memory capacity and cognitive functioning score.

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On May 25, 2010, LiveScience published an article titled "Simple Memory Test Predicts Intelligence." The article summarized a study that found that the score on a test of working memory capacity was correlated with a number of different measures of intelligence. One measure was cognitive functioning score. Suppose that one such linear regression for working memory capacity and cognitive functioning score from a sample of 12 people is 
ŷ = 6.2 + 26.7x,
 where y is the cognitive functioning score and x is the working memory score.
(a)
In a hypothesis test for the slope of the linear regression, which of the following would be the correct alternative hypothesis?
Ha: ? = 0
Ha: ? > 26.7
    
Ha: ? ≠ 0
Ha: ? < 26.7
(b)
Given the standard error of the slope, 5.2, calculate the test statistic. (Round your answer to four decimal places.)
 
(c)
Calculate the P-value and determine which conclusion is correct for the hypothesis test based on 
? = 0.05.
 (Use technology.)
We would reject the null hypothesis. There is insufficient evidence of a linear relationship between working memory capacity and cognitive functioning score.We would fail to reject the null hypothesis. There is insufficient evidence of a linear relationship between working memory capacity and cognitive functioning score.    We would reject the null hypothesis. There is sufficient evidence of a linear relationship between working memory capacity and cognitive functioning score.We would fail to reject the null hypothesis. There is sufficient evidence of a linear relationship between working memory capacity and cognitive functioning score.
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