find the two-tailed question

Question

a student takes a sample of n=30 books and records the publication date for each. The sample produces an average of M=23.8 years with a variance of s square=67.5. Use this sample to conduct a one-tailed test with .01 to determine whether the average age of the library books is significantly greater than 20 years

Answer 1

Null Hypothesis:  age > 20

Alternative Hypothesis: age <=20

 

std-dev = square-root( variance/ (n-1) ) =   square-root ( 67.5 / 29) 

 

test statistic:      (X - mean)/stddev =  (20 - 23.8)/1.5256428831

 

                                                       = -3.8/ 1.5256428834

 

                                                        = -2.49075

 

The  99% confidence threshold for a one-tailed test assuming normal distribution is -2.325.

There is enough statistical evidence to Reject the Null Hypothesis.

No significant evidence that the average age of the library books are greater than 20 years.