After a quick inspection of the gradebook, Professor Hulbert believes the mean e

Question

After a quick inspection of the gradebook, Professor Hulbert believes the mean exam score of his students is 70. Professor Hulbert picks 10 students at random and records their exam scores below.

80, 80, 80, 85, 85, 85, 85, 90, 90, 90

a. Assume a standard deviation of 10 for the exam scores. At the 10% significance level, is there enough evidence to conclude the mean exam score of his students is more than 70?

b. Without using the assumption above the standard deviation for the exam scores, at the 5% significance level, is there enough evidence to conclude the mean exam score of his students is different from 70?

Explanation / Answer

80 80 Ho : miu = 70 80 Ha : miu > 70 85 85 t = ( 85 - 70 ) / ( 4.08 / srqt 10 ) 85 t = 11.63 85 p value : 0.0000 90 since p value is lower than 0.10 ( significance leve) 90 we reject Ho 90 conclusion there is sufficient evidence to support the claim x-bar 85 that mean is greater than 70 SD 4.08 n 10 since p value is lower than 0.05 we reject Ho conclusion the mean is different from 70

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