Problem: A team of software engineers are testing the time taken for a particular type of modern computer to execute a complicated algorithm for factoring large numbers. They know that the mean time to execute the algorithm was 1,150 seconds. However, the algorithm has recently been upgraded and it is suspected that the mean time has now been decreased because of the improvements made. They would like to test this hypothesis.
A random sample of 40 times are collected:
Download the data
|
749
|
644
|
463
|
424
|
1,118
|
937
|
951
|
841
|
962
|
1,066
|
|
1,056
|
867
|
400
|
970
|
625
|
821
|
976
|
789
|
948
|
656
|
|
961
|
677
|
664
|
1,147
|
798
|
847
|
1,012
|
1,160
|
616
|
800
|
|
658
|
873
|
1,099
|
694
|
1,103
|
988
|
1,058
|
723
|
744
|
513
|
You may find this Student's t distribution table useful throughout this question.
a) Calculate the test statistic (t) for the hypothesis test. Give your answer to 4 decimal places.
t =
b) At a level of significance of α = 0.1, the result of this test is that the null hypothesis is rejected not rejected.