Question

A head librarian supervises a number of libraries in a large county. He wants to know if full-time library workers and part-time library workers re-shelve books at the same rate. So, he checks the records of 35 full-time library workers and finds that they re-shelve an average of 190 books per hour with a standard deviation of 18.3 books per hour. The records of 35 part-time library show that they re-shelve an average of 180 books per hour with a standard deviation of 14.4 books per hour.

Using a level of significance of ?=.05, is there enough evidence to indicate a difference in the mean number of books re-shelved by full-time workers compared to part-time workers?

Answer 1

Null hypothesis: There is no significant difference in the mean number of books re-shelved by full-time workers compared to part-time workers.

Alternate hypothesis: There is significant difference in the mean number of books re-shelved by full-time workers compared to part-time workers.

Appropriate test: The appropriate test to be used is the independent samples t-test for means.

Assumptions:

i) The samples are random and independent to each other.

ii) The samples are drawn from normal populations.

iii) The samples are drawn from populations of homogenous variances.

Test statistic:

Observed test statistic:

Level of significance and critical values:

The level of significance is and the test is two tailed test. The left and right critical values for t₆₈ distribution at 5% level of significance are -1.995 and +1.995 respectively.

Decision rule:

The null hypothesis can be rejected if the observed test statistic falls outside the critical region or the p-value of the observed test statistic is lesser than the level of significance.

Conclusion:

The observed test statistic value is 2.526 and it falls outside the critical regions (-1.995, +1.995). So there is sufficient evidence to reject the null hypothesis at 5% level of significance. It can be concluded that there is enough evidence to indicate a difference in the mean number of books re-shelved by full-time workers compared to part-time workers.