Do taller adults make more money? The authors of a paper investigated the association between height and earnings. They used the simple linear regression model to describe the relationship between x = height (in inches) and y = log(weekly gross earnings in dollars) in a very large sample of men. The logarithm of weekly gross earnings was used because this transformation resulted in a relationship that was approximately linear. = The paper reported that the slope of the estimated regression line was b = 0.027 and the standard deviation of b was sp 0.002. Carry out a hypothesis test using a = 0.05 to decide if there is convincing evidence of a useful linear relationship between height and the logarithm of weekly earnings. Assume that the basic assumptions of the simple linear regression model are reasonably met. State the appropriate null and alternative hypotheses. Hoi B < 0 H₂ B > 0 O Ho: B = 0 ○ a' Ho: B > O HBO Ha ○ Ho: B = 0 Hạ: B < 0 = 0 ○ Ho: B Ha B > 0 a' Find the test statistic and P-value. (Assume that the sample size is large enough to use the normal distribution. Round your test statistic to one decimal place and your P-value to three decimal places.) t = P-value = What can you conclude? Reject Ho. We do not have convincing evidence of a useful linear relationship between height and the logarithm of weekly earnings. Reject Ho. We have convincing evidence of a useful linear relationship between height and the logarithm of weekly earnings. Fail to reject Ho. We have convincing evidence of a useful linear relationship between height and the logarithm of weekly earnings. Fail to reject Ho. We do not have convincing evidence of a useful linear relationship between height and the logarithm of weekly earnings.

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