Representing Data Effectively
Problem 1. (Hypothetical) The General Social Survey measures the number of hours that individuals spend on the internet each week. Males use the Internet 14.0 hours per week. (Standard deviation 10.0; N = 220), while women use the Internet 10.0 hours per week (standard deviation 10.50; N = 190).
Test the research hypothesis that men use the internet more hours than women. Set alpha at .05.
Would your decision have been different if alpha were set at .01?
Given that,
Males use the Internet () = 14.0hours
Women use the Internet () =10.0hours
Standard deviation () =10.0
Standard deviation () =10.50
= 220
= 190
Five – step model: Step-1. Firstly we have to setup the null hypothesis.
Step-2. Secondly we set the criteria of the problem.
Step-3. Thirdly, obtain the samples and statistic.
Step-4. Fourthly we have to compare the sample to the hypothesis.
Step-5. Lastly we have to make our conclusion.
Now, we set up the null hypothesis
: Men use the internet more hours than women.
i.e. >
: Men does not use the internet more than woman
i.e. ≤
The test statistic is calculated as
d =
=
=
=3.933
Degrees of freedom= +-2
=220+190-2
=408
P-value = 3.72857E-05
Since P-value <α-value.
We clearly reject .Therefore there is a sufficient evidence at 5% level of significance to conclude that Men use the internet more hours than women.
(b) No, the decision have not been different if alpha were set at .01 i.e. 1%. Because here P-value < α-value.
2. (Hypothetical): This is your research question: Is there a significant difference in the level of community service participation between criminal justice majors and accounting majors?
What is your research hypothesis? Should you conduct a one tailed or a two tailed test? Why?
Your study finds that 34% of 220 criminal justice majors reported volunteering in the previous month, compared with 24% of 190 accounting majors.
Present the five-step model, testing your hypothesis at the .05 level. What do you conclude?
Would your decision have been different if alpha were set at .01?
We know that there are two types of hypothesis. One is null hypothesis and the other is alternative hypothesis. Null hypothesis is denoted by and alternative hypothesis.
: There is a significant difference in the level of community service participation between criminal justice majors and accounting majors.
: There is no significant difference in the level of community service participation between criminal justice majors and accounting majors.
We will conduct two tailed test. Because we are interested to know whether the values are less than or greater than and unequal.
Five – step model: Step-1. Firstly we have to setup the null hypothesis.
Step-2. Secondly we set the criteria of the problem.
Step-3. Thirdly, obtain the samples and statistic.
Step-4. Fourthly we have to compare the sample to the hypothesis.
Step-5. Lastly we have to make our conclusion.
(b)
: There is a significant difference in the level of community service participation between criminal justice majors and accounting majors.
.e. =
: There is no significant difference in the level of community service participation between criminal justice majors and accounting majors.
.e.
We know that
Z=
Where =220
=190
=0.34
=0.24
=0.34*220
=74.8
=0.24*190
=45.6
P=
=220*0.34+190*0.24/220+190
=0.29
Degrees of freedom=408
Now the statistic value,
Z=
?z=5.11
Since ?Z? calculated≥ ?Z? tabulated at 408 d.f.
We clearly reject .Therefore there is a sufficient evidence at 5% level of significance to conclude that there is no significant difference in the level of community service participation between criminal justice majors and accounting majors.
Since P- value≤α-value.
The decision have not been different if alpha were set at .01.That isWe clearly reject .Therefore there is a sufficient evidence at 5% level of significance to conclude that there is no significant difference in the level of community service participation between criminal justice majors and accounting majors.
References:
Bonett, D. G., & Wright, T. A. (2015). Cronbach’s alpha reliability: Interval estimation, hypothesis testing, and sample size planning. Journal of Organizational Behavior, 36(1), 3-15.
Chwialkowski, K. P., Ramdas, A., Sejdinovic, D., & Gretton, A. (2015). Fast two-sample testing with analytic representations of probability measures. In Advances in Neural Information Processing Systems (pp. 1981-1989).
Park, H. M. (2015). Hypothesis testing and statistical power of a test.
van den Heuvel, M. P., de Lange, S. C., Zalesky, A., Seguin, C., Yeo, B. T., & Schmidt, R. (2017). Proportional thresholding in resting-state fMRI functional connectivity networks and consequences for patient-control connectome studies: Issues and recommendations. Neuroimage, 152, 437-449.
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