# Question: A model relating fertilizer use to cotton yield is estimated

A model relating fertilizer use to cotton yield is estimated using 62 observations, and the following estimates are obtained:

= 15.43 + 0.12 (3.2431) (0.0371)

Where Y is the cotton yield in bushels/acre and X is the amount of fertilizer used in lb/acre. Standard errors of estimates are given in parentheses.

A: Formulate the appropriate null hypothesis, and alternative hypothesis, to test if fertilizer use has a positive effect on cotton yield. Calculate the test statistic and perform the test at 5 percent significance level. What is your conclusion?

B: Suppose the null hypothesis you constructed in part A is true. What is the probability of a Type I error?

= 15.43 + 0.12 (3.2431) (0.0371)

Where Y is the cotton yield in bushels/acre and X is the amount of fertilizer used in lb/acre. Standard errors of estimates are given in parentheses.

A: Formulate the appropriate null hypothesis, and alternative hypothesis, to test if fertilizer use has a positive effect on cotton yield. Calculate the test statistic and perform the test at 5 percent significance level. What is your conclusion?

B: Suppose the null hypothesis you constructed in part A is true. What is the probability of a Type I error?

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