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webwork / math243fall-masden /week 8b - ch20 inference about a population mean / 3 Week 8b - Ch20 Inference About a Population Mean: Problem 3 Previous Problem ListNext (1 point) An agricultural field trial compares the yield of two varieties of com. The researchers divide in half each of 10 fields of land in different locations and plarnt each corn variety in one half of each plot. After harvest, the yields are compared in bushels per acre at each location. The 10 differences (Variety A- Variety B) give 1.68 and s4.61. Does this sample provide evidence that Variety A had a higher yield than Variety B? (a State the null and alternative hypotheses Type mu" for the symbol μ e.g. mu > 1 for the mean is greater than 1, mu < 1 for the mean is less than 1 mu not 1 for the mean is not equal to 1) Ho Ha (b) Find the test statistic, t (c) Answer the question: Does this sample provide evidence that Variety A had a higher yield than variety B? (Use a 5% level of significance) (Type: Yes or No) Note: You can earn partial credit on this probiem. Preview My Answers Submit Answers You have attempted this problem 0 times. You have unlimited attempts remaining

Answer 1

Data:     

n = n1 = n2 = 5    

d-bar = 1.68    

s (of d) = 4.61    

Hypotheses:     

Ho: d-bar ≥ 0    

Ha: d-bar < 0    

Decision Rule:     

α = 0.05    

Degrees of freedom = 5 - 1 = 4

Critical t- score = -2.131846782   

Reject Ho if t < -2.131846782    

Test Statistic:     

SE = s/√n = 4.61/√5 = 2.061654675   

t = d-bar/SE = 1.68/2.06165467525481 = 0.814879436   

p- value = 0.230438158    

Decision (in terms of the hypotheses):    

Since 0.814879436 > -2.132 we fail to reject Ho

Conclusion (in terms of the problem):    

There is no sufficient evidence that variety A had a higher yield than variety B.

ANSWERS:

(a) Ho: mu1 > mu2 and Ha: mu1 < mu2

(b) t = 0.815

(c) No