Order ID:89JHGSJE83839 | Style:APA/MLA/Harvard/Chicago | Pages:5-10 |
Instructions:
Hypothesis Test for Difference in Two Population Means
Learn by Doing
In this activity you will learn to use StatCrunch to perform a two-sample t-test.
Some features of this activity may not work well on a cell phone or tablet. We highly recommend that you complete this activity on a computer.
Here are the directions and grading rubric for the discussion board exercises.
A list of StatCrunch directions is provided at the bottom of this page.
Context
Do undergraduates sleep less than graduate students?
A student conducted a study of sleep habits at a large state university. His hypothesis is that undergraduates will party more and sleep less than graduate students. He surveyed random samples of 75 undergraduate students and 50 graduate students. Subjects reported the hours they sleep in a typical night.
For this hypothesis test, he defined the population means as follows:
μ 1 is the mean number of hours undergraduate students sleep in a typical night.
μ 2 is the mean number of hours graduate students sleep in a typical night.
Variables
Hours: typical number of hours a student sleeps each night
Program: undergraduate or graduate
Program is the explanatory variable, and the data is categorical. Hours is the response variable, and the data is quantitative.
Data
Two sample T hypothesis test:
μ1 : Mean of undergraduate
μ2 : Mean of graduate
μ1 – μ2 : Difference between two means
H0 : μ1 – μ2 = 0
HA : μ1 – μ2 < 0
(without pooled variances)
Hypothesis test results:
Difference | Sample Diff. | Std. Err. | DF | T-Stat | P-value |
μ1 – μ2 | -0.23333333 | 0.18963708 | 106.32776 | -1.2304204 | 0.1106 |
Prompt
State the null and alternative hypotheses. Include a clear description of the populations and the variable.
Explain why we can safely use the two-sample T-test in this case.
Use StatCrunch to carry out the test.
Copy and paste the content of in the StatCrunch output window (text and the table) in your initial post.
State a conclusion in the context of this problem.
ANSWER(S): (hint)
Since we want to check whether the data supports the claim that undergraduate students sleep less, on average, than graduate students, we are testing: H 0 : μ 1 − μ 2 = 0 H a : μ 1 − μ 2 < 0
We can safely use the two-sample T-test in this case since:
Both samples are random, and therefore independent.
The sample sizes (75 and 50) are quite large, and therefore we can proceed regardless of whether the populations are normal or not.
T = -1.23; P-value = 0.111
Here is the StatCrunch output depicting these values.
Two sample T hypothesis test:
μ 1 : Mean of undergraduate
μ 2 : Mean of graduate
H 0 : μ 1 − μ 2 = 0
H a : μ 1 − μ 2 < 0
(without pooled variances)
Hypothesis test results: | |||||
Difference | Sample Diff. | Sd. Err. | DF | T-Stat | P-Value |
μ1 – μ2 | -0.23333333 | 0.18963708 | 106.32776 | -1.2304204 | 0.1106 |
The P-value (0.111) is greater than 0.05. This indicates that the observed data is not unusual if undergraduate and graduate students, on average, have the same mean for sleep hours. Therefore, the data do not provide evidence to reject H 0 . So we cannot conclude that undergraduate students sleep less, on average, than graduate students.
RUBRIC |
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Excellent Quality 95-100%
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Introduction
45-41 points The background and significance of the problem and a clear statement of the research purpose is provided. The search history is mentioned. |
Literature Support 91-84 points The background and significance of the problem and a clear statement of the research purpose is provided. The search history is mentioned. |
Methodology 58-53 points Content is well-organized with headings for each slide and bulleted lists to group related material as needed. Use of font, color, graphics, effects, etc. to enhance readability and presentation content is excellent. Length requirements of 10 slides/pages or less is met. |
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Average Score 50-85% |
40-38 points More depth/detail for the background and significance is needed, or the research detail is not clear. No search history information is provided. |
83-76 points Review of relevant theoretical literature is evident, but there is little integration of studies into concepts related to problem. Review is partially focused and organized. Supporting and opposing research are included. Summary of information presented is included. Conclusion may not contain a biblical integration. |
52-49 points Content is somewhat organized, but no structure is apparent. The use of font, color, graphics, effects, etc. is occasionally detracting to the presentation content. Length requirements may not be met. |
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Poor Quality 0-45% |
37-1 points The background and/or significance are missing. No search history information is provided. |
75-1 points Review of relevant theoretical literature is evident, but there is no integration of studies into concepts related to problem. Review is partially focused and organized. Supporting and opposing research are not included in the summary of information presented. Conclusion does not contain a biblical integration. |
48-1 points There is no clear or logical organizational structure. No logical sequence is apparent. The use of font, color, graphics, effects etc. is often detracting to the presentation content. Length requirements may not be met |
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Hypothesis Test for Difference in Two Population Means |
Hypothesis Test for Difference in Two Population Means