Your statistics instructor often ponders the relationship between commute time and job satisfaction while driving back and forth to campus. Your instructor hypothesizes that people with a shorter commute time will have higher degrees of job satisfaction. Randomly sampling 600 Valley commuters, the instructor finds the following data listed in frequencies: Table 2: Commuters by Length of Commute and Job Satisfaction
Your statistics instructor often ponders the relationship between commute time and job satisfaction while driving back and forth to campus. Your instructor hypothesizes that people with a shorter commute time will have higher degrees of job satisfaction. Randomly sampling 600 Valley commuters, the instructor finds the following data listed in frequencies:
Table 2: Commuters by Length of Commute and Job Satisfaction
|
Job Satisfaction |
Number Who Commute 20 Minutes or Less |
Number Who Commute 21 to 40 Minutes |
Number Who Commute 41 Minutes or More |
Total Number for Each Level of Job Satisfaction |
|
Dissatisfied |
10 |
60 |
140 |
210 |
|
Neutral |
45 |
59 |
51 |
155 |
|
Satisfied |
145 |
60 |
30 |
235 |
|
Total Number for Each Commute Time |
200 |
179 |
221 |
600 |
Your instructor calculates a chi-square of 202.5 with four degrees of freedom.
In a detailed paragraph of at least eight sentences, discuss whether the percent distribution of the cross-tab and chi-square support, or do not support, the instructor’s hypothesis. Ensure that you mention
-
- The null hypothesis
- The IV, DV, UA, and direction of relationship
- How the IV percent distribution changes in relation to the DV
- What level of significance you will use, and how the chi-square statistic obtained from the sample compares to its critical value
- Whether the results obtained from the sample are statistically significant, and how accurately the results would reflect the population
State the test hypotheses:
The two categories of interest are the “Length of commute” and “Job satisfaction”.
The researcher is specially interested to test whether there is an association between the categories “Length of commute” and “Job satisfaction”.
Thus, the study seeks to find whether there is any association between the two categories “Length of commute” and “Job satisfaction”. In other words, the study aims to test whether the two categories “Length of commute” and “Job satisfaction” are independent or not, using a Chi-square test of Independence.
The hypotheses to be tested are:
Null hypothesis:
H0: The two categories “Length of commute” and “Job satisfaction” are independent.
Alternative hypothesis:
Ha: The two categories “Length of commute” and “Job satisfaction” are dependent.
Variable of interest:
The two variables of interest are “Length of commute” and “Job satisfaction”.
The independent variable is Length of commute time.
The dependent variable is Job satisfaction.
Level of significance: Level of significance is the probability of rejecting the null hypothesis H0, when the null hypothesis H0 is true.
Since, the level of significance is not specified, the prior level of significance α = 5% = 5/100 = 0.05 can be used.
Thus, the level of significance is α = 0.05.
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