A labor union is appealing for more vacation time for its workers, claiming that worker productivity is affected by whether or not they have taken a vacation recently. The following table lists how many workers fall in each level of production rates (categorized as low, medium, or high rate of production) for a sample of 1250 employees based on whether they had a vacation recently. recent vacation no vacation total low rate medium rate high rate 157 243 185 - 331 342 574 163 171 334 If there was no relationship between vacation status and productivity (that is, the two variables are independent/ not associated) ... How many recently vacationed workers in the sample would we expect to have a high production rate? 258.52960 (round to 3 decimal places) Test statistic: x² = How many of the low-rate-of-production workers in the sample would we expect to have not had a vacation? 187.963 o(round to 3 decimal places) critical x² total 563 687 1250 Using the following hypotheses, Ho: there is no relationship between vacation status & worker productivity Ha: worker productivity depends on vacation status (there is a relationship) Perform a x² hypothesis test for association at the a= 0.01 level of significance. p-value: p = (round to 3 decimal places) (round to 3 decimal places) (round to 3 decimal places) The conclusion of the test is: O reject Ho. So there is statistically significant evidence that worker productivity depends on taking vacation. O fail to reject Ho. The union's sample did not provide statistically significant evidence of a relationship between productivity and vacation status. O reject Ho. The union has proven that worker productivity depends on taking vacation.
A labor union is appealing for more vacation time for its workers, claiming that worker productivity is affected by whether or not they have taken a vacation recently. The following table lists how many workers fall in each level of production rates (categorized as low, medium, or high rate of production) for a sample of 1250 employees based on whether they had a vacation recently. recent vacation no vacation total low rate medium rate high rate 157 243 185 - 331 342 574 163 171 334 If there was no relationship between vacation status and productivity (that is, the two variables are independent/ not associated) ... How many recently vacationed workers in the sample would we expect to have a high production rate? 258.52960 (round to 3 decimal places) Test statistic: x² = How many of the low-rate-of-production workers in the sample would we expect to have not had a vacation? 187.963 o(round to 3 decimal places) critical x² total 563 687 1250 Using the following hypotheses, Ho: there is no relationship between vacation status & worker productivity Ha: worker productivity depends on vacation status (there is a relationship) Perform a x² hypothesis test for association at the a= 0.01 level of significance. p-value: p = (round to 3 decimal places) (round to 3 decimal places) (round to 3 decimal places) The conclusion of the test is: O reject Ho. So there is statistically significant evidence that worker productivity depends on taking vacation. O fail to reject Ho. The union's sample did not provide statistically significant evidence of a relationship between productivity and vacation status. O reject Ho. The union has proven that worker productivity depends on taking vacation.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:A labor union is appealing for more vacation time for its workers, claiming that worker productivity is affected
by whether or not they have taken a vacation recently. The following table lists how many workers fall in each
level of production rates (categorized as low, medium, or high rate of production) for a sample of 1250
employees based on whether they had a vacation recently.
recent vacation
no vacation
total
low rate medium rate
157
185
342
If there was no relationship between vacation status and productivity (that is, the two variables are
independent/ not associated) ...
p-value: p =
163
171
334
How many recently vacationed workers in the sample would we expect to have a high production rate?
258.5296 (round to 3 decimal places)
Ꮕ
Test statistic: x² =
How many of the low-rate-of-production workers in the sample would we expect to have not had a vacation?
187.963 (round to 3 decimal places)
✔
critical x²
Using the following hypotheses,
Ho: there is no relationship between vacation status & worker productivity
Ha: worker productivity depends on vacation status (there is a relationship)
Perform a x² hypothesis test for association at the a= 0.01 level of significance.
=
high rate total
563
687
1250
20-2-2
243
331
574
(round to 3 decimal places)
(round to 3 decimal places)
M
(round to 3 decimal places)
The conclusion of the test is:
O reject Ho. So there is statistically significant evidence that worker productivity depends on taking
vacation.
O fail to reject Ho. The union's sample did not provide statistically significant evidence of a relationship
between productivity and vacation status.
reject Ho. The union has proven that worker productivity depends on taking vacation.
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