STAT 251-03
Lab 5 Report
Symbols for possible use: [pic], π, [pic], μ, σ, s
[pic]
Descriptive Statistics:
(a) Produce numerical and graphical summaries of your sample data. [Make sure your graph has a title and/or axis label.]
Paste a copy of your output here.
(b) Write a paragraph summarizing the distribution of sleep time responses in this sample. (Make sure you discuss (with supporting evidence) shape, center, spread (using appropriate symbols), outliers and other unusual observations, and sample size, and that sure your comments are in context.)
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(c) Does the shape of the distribution behave as you expected in the pre-lab?
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(d) Do the data provide preliminary evidence that students at your school tend to less than 8 hours of sleep on a typical night?
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[pic]
Population Model:
(e) Do we know the value of the population mean amount of sleep on a typical night for all students at your school? What symbol can we use to represent its value?
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The research conjecture is that students at your school average less than 8 hours of sleep a night.
(f) Translate the above statement to null and alternative hypothesis statements (Ho and Ha) (write out hypotheses in both symbols and in words).
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(g) Do we know the value of the population standard deviation? What symbol can we use to represents its value? Provide a one-sentence interpretation of what this value would represent in this context.
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[pic]
Population Model/ Central Limit Theorem:
|Population Shape |Normal (h) |Right skewed (j) |
| |Paste (and shrink) screen capture of graph of sample |Paste screen capture here |
| |means | |
|Shape | | |
|Mean | | |
|Std. Deviation | | |
|Approx p-value | | |
(i) Why did we count below instead of above?
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(k) Did the assumed shape of the population distribution of sleep times make a substantial difference in the shape, center, or spread of the distribution of sample means? In the approximate p-value? That is, did it really matter what the shape of the population distribution was? Explain.
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(l) Is the sample size from our study of sleep times large enough for us to assume that the shape of the distribution of sample means will be approximately normal? Justify your answer.
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[pic]
Statistical Inference:
(m) Regardless of your answer to (l) (for practice), use technology to calculate the test statistic and p-value.
Paste screen capture here.
(n) Provide an interpretation of the "test statistic" provided in the output.
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(o) Report the relevant p-value. Provide an interpretation of this p-value in this context. Hint: The proportion of random samples that... assuming ....
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(p) Based on this p-value (and the standard cut-off values from Lab 1), how much evidence do the sample data provide against the null hypothesis?
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(q) Provide a one sentence interpretation of the confidence interval. Hint: What is supposed to be in the interval?
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[pic]
Application:
(r) Now repeat the analysis to test the research conjecture that that the average amount of sleep by all students at your school on a typical night differs from 7 hours.
Paste a copy of your output here.
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(s) Now reconsider your confidence interval for the population mean from before (question u). Based on this interval, could you have predicted how this test of significance would have turned out? Explain.
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(t) What does the confidence interval tell you about how students at your school compare to the website's claim in the pre-lab that college students average 6-6.9 hours of sleep a night?
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[pic]
Summary:
(u) Summarize (in a paragraph) what you have learned in this lab about the sleep habits on a typical night of all students at your school. (There will be some repetition from what you have said earlier.) If you have any concerns about the “technical conditions” of the analysis procedures we used, state them now. In particular,
• Validity: Do you consider the conditions necessary for the Central Limit Theorem to have been met? Explain.
• Significance: Is 8 a plausible value for the average amount of sleep on a typical night by all students at your school? Is 7?
• Estimation (confidence): What are plausible values? How do students at your school compare to the 6-6.9 hours averaged by college students overall?
• Generalizability: Any concerns about generalizing our sample results to the larger population of all students at your school?
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