Hypothesis Test for Difference in Two Population Means
Order ID 53563633773 Type Essay Writer Level Masters Style APA Sources/References 4 Perfect Number of Pages to Order 5-10 Pages Description/Paper 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 graduateProgram 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
QUALITY OF RESPONSE NO RESPONSE POOR / UNSATISFACTORY SATISFACTORY GOOD EXCELLENT Content (worth a maximum of 50% of the total points) Zero points: Student failed to submit the final paper. 20 points out of 50: The essay illustrates poor understanding of the relevant material by failing to address or incorrectly addressing the relevant content; failing to identify or inaccurately explaining/defining key concepts/ideas; ignoring or incorrectly explaining key points/claims and the reasoning behind them; and/or incorrectly or inappropriately using terminology; and elements of the response are lacking. 30 points out of 50: The essay illustrates a rudimentary understanding of the relevant material by mentioning but not full explaining the relevant content; identifying some of the key concepts/ideas though failing to fully or accurately explain many of them; using terminology, though sometimes inaccurately or inappropriately; and/or incorporating some key claims/points but failing to explain the reasoning behind them or doing so inaccurately. Elements of the required response may also be lacking. 40 points out of 50: The essay illustrates solid understanding of the relevant material by correctly addressing most of the relevant content; identifying and explaining most of the key concepts/ideas; using correct terminology; explaining the reasoning behind most of the key points/claims; and/or where necessary or useful, substantiating some points with accurate examples. The answer is complete. 50 points: The essay illustrates exemplary understanding of the relevant material by thoroughly and correctly addressing the relevant content; identifying and explaining all of the key concepts/ideas; using correct terminology explaining the reasoning behind key points/claims and substantiating, as necessary/useful, points with several accurate and illuminating examples. No aspects of the required answer are missing. Use of Sources (worth a maximum of 20% of the total points). Zero points: Student failed to include citations and/or references. Or the student failed to submit a final paper. 5 out 20 points: Sources are seldom cited to support statements and/or format of citations are not recognizable as APA 6th Edition format. There are major errors in the formation of the references and citations. And/or there is a major reliance on highly questionable. The Student fails to provide an adequate synthesis of research collected for the paper. 10 out 20 points: References to scholarly sources are occasionally given; many statements seem unsubstantiated. Frequent errors in APA 6th Edition format, leaving the reader confused about the source of the information. There are significant errors of the formation in the references and citations. And/or there is a significant use of highly questionable sources. 15 out 20 points: Credible Scholarly sources are used effectively support claims and are, for the most part, clear and fairly represented. APA 6th Edition is used with only a few minor errors. There are minor errors in reference and/or citations. And/or there is some use of questionable sources. 20 points: Credible scholarly sources are used to give compelling evidence to support claims and are clearly and fairly represented. APA 6th Edition format is used accurately and consistently. The student uses above the maximum required references in the development of the assignment. 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