A statistics teacher believes that students who take the evening statistics clas

Question

A statistics teacher believes that students who take the evening statistics class score lower than the students who take a day class. The results of a special exam are shown below. Assume that the two samples are random and independent. Can the teacher conclude that the evening students score lower, in general? Use = 0.01.

(a) State the null and alternate hypotheses. Is this a left-tailed, right-tailed, or two-tailed test?
(b) What sampling distribution should be used (standard normal or Student’s t)? Explain your reasoning.
(c) Determine the P-value. (Assume that the population variances are dierent.)
(d) According to your result, will you reject or fail to reject the null hypothesis? Explain and interpret what the result then tells you in terms of day versus evening students.

Explanation / Answer

Ho : p1 = p2

Ha : p1 > p2

P1 : days students

P2 = evening students

P1 = 37 / 75 = 0.49

P2 = 40 / 72 = 0.55

P = ( 37+40) / (75+72) = 0.5238

Z = ( 0.49 - 0.55 ) / ( srqt 0.5238*0.4762* ( 1/75 + 1/72 ) )

Z = -0.73

p value : 1 - 0.2643 = 0.7357

since p value is greater than alpha we fail to reject Ho

there is no evidence to conclude that evening statistics class score lower than the students who take a day class

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