Question

Suppose an editor of a publishing company claims that the mean time to write a textbook is at most 15 months. A sample of 16 textbook authors is randomly selected and it is found that the mean time taken by them to write a textbook was 12.5. Assume also that the standard deviation is known to be 3.6 months. Assuming the time to write a textbook is normally distributed and using a 0.05 level of significance, would you conclude the editor’s claim is true?

Answer 1

To test,

H₀ : The mean time to write a textbook is 15 months

Vs

H₁: The mean time to write a textbook is atmost 15 months

i.e.,

Test statistic:

Given,

Thus,

  

Thus, test statistic z= -2.78

For p-value, using standard normal probability table, the P(z< -2.77) =  0.00272 (This is the one sided p-value)

Hence, the two sided p-value is = 2 * 0.00272 = 0.00544

Given level of significance, = 0.05

Decision Rule: If p-value > 0.05, we accept Ho, otherwise we reject Ho.

Here, p-value=0.0054 < = 0.05 , hence we reject Ho

Therefore, we conclude that the editor's claim is true at 5% level of significance.