Question

A company wants to estimate the time for employees to complete a task with three different types of training. Sample times to complete the task are as follows:

Sample trained by method A = 20 minutes s = 1.73 minutes s2 = 3 minutes sample size n = 20
Sample trained by method B = 22 minutes s = 1.73 minutes s2 = 3 minutes sample size n = 20
Sample trained by method C = 18 minutes s = 1.73 minutes s2 = 3 minutes sample size n = 20
Mean of all data values for all samples pooled = = 20 minutes
Can you prove, at 95% confidence, that the times to complete the task are different for employees who have been trained by different methods? To get full credit, state your null and alternate hypothesis, show how you calculated your test statistic, show your reject region, and state your conclusion: are the times different for employees trained by different methods? Answer YES or NO

Answer 1

To determine if the times to complete the task are different for employees trained by different methods, we can use an analysis of variance (ANOVA) test.

Step-by-step explanation:

To test if the times to complete the task are different for employees who have been trained by different methods, we can use an analysis of variance (ANOVA) test. The null hypothesis is that there is no difference in the mean time for employees trained by different methods. The alternative hypothesis is that there is a difference in the mean time.

To calculate the test statistic, we use the F-test. The F-test compares the variation between the groups to the variation within the groups. If the test statistic is greater than the critical value, we reject the null hypothesis.

Since the sample sizes for each group are equal and the sample variances are equal, we can use the pooled variance formula to calculate the test statistic. The test statistic is given by F = (between group variance)/(within group variance).

If the calculated F-value is greater than the critical value from the F-distribution table, we reject the null hypothesis and conclude that the times to complete the task are different for employees trained by different methods. If the calculated F-value is less than or equal to the critical value, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest a difference in the mean time for employees trained by different methods.