Question

A supervisor of a textile industry collected information regarding the mean number of hours of productive work done by a random sample of ten workers in a month. After the performance bonus was announced by management, the supervisor again collected the information of the mean number of hours of productive work done by the same ten workers the next month. The results are summarized below. Worker 1 2 3 4 5 6 7 8 9 10 Before bonus 6.8 6.2 7.4 6.9 7.1 6.5 6 6.5 7.5 6.7 After bonus 7 6.5 7.5 7 7.3 6.7 6.4 6.9 7.3 6.9 Identify the correct decision regarding the null hypothesis at the 1% significance level

Answer 1

Answer:

There is sufficient statistical evidence to state that the average hours of productive work, after announcing the stimulus, has increased significantly

Step-by-step explanation:

To solve this problem, we run a hypothesis test about the difference between population means with dependent samples. Consider the differences in average hours of productive work after the stimulus minus average hours of productive work before the stimulus.

Difference in the null hypothesis (Do) = 0

Sample size (n) = 10

Mean of the sample differences (DM) = 0.19

Standard deviation of the sample differences (SM) = 0.1729

Significance level = 0.01

H0: Do = 0

Ha: Do> = 0

Test statistic = $(DM - Do) / [SM / \sqrt {n}]$

Right critical T value (for 0.01) = 2.8214

Calculated statistic = $(0.19 - 0) / [0.1729 / \sqrt {10}] = 3.47503$

p-value = 0.00350

Since, the value of the test statistic is greater than the value of the calculated statistic, the null hypothesis is rejected. There is sufficient statistical evidence to state that the average hours of productive work, after announcing the stimulus, has increased significantly. The p - value is 0.00350.