Description
You will be assigned one column of quantitative (numerical measurement) data from the following excel spreadsheet. You will be doing a one-population mean hypothesis test (T-test) with your data. See directions below. Make sure you follow the directions and answer all of the required questions. You do not need to write the questions. You can just type or write the answers. You will be writing your null and alternative hypothesis, checking conditions, calculating the standard error and T-test statistic, and using StatKey at www.lock5stat.com to create graphs, sample statistics, and use the T-distribution to calculate the critical value and the P-value. You will also be writing sentences to explain the T-test statistic, significance, sampling variability, P-value and the conclusion.TEXTBOOK LINK, COLUMN OF DATA, ASSIGNED HYPOTHESIS CLAIM, PROJECT DIRECTIONS, and GRADING RUBRIC WILL BE FOUND BELOW IN THE ATTACHED FILES.
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Math 140 Project: One-Population Mean Hypothesis Test
You will be assigned one column of quantitative (numerical measurement) data from the
following excel spreadsheet. You will be doing a one-population mean hypothesis test
(T-test) with your data. See directions below. Make sure you follow the directions and
answer all of the required questions. You do not need to write the questions. You can
just type or write the answers. You will be writing your null and alternative hypothesis,
checking conditions, calculating the standard error and T-test statistic, and using
StatKey at www.lock5stat.com
to create graphs, sample statistics, and use the T-distribution to calculate the critical
value and the P-value. You will also be writing sentences to explain the T-test statistic,
significance, sampling variability, P-value and the conclusion.
Link to
textbook:https://archive.org/details/intro_to_stats_for_community_college_students_by_
Matt_Teachout_complete_book
Assigned Hypothesis Test Claim and Alternative Hypothesis (Ha)
The population mean average height in inches of all men is less than
70 inches.
Math 140 PROJECT Directions and Grading Rubric
One-Population Mean Hypothesis T-Test
(Use with Teachout textbook Chapter 3)
PROJECT GRADING RUBRIC
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First and Last name, Project title, Instructor’s Name, Section#, Semester and Year (2 points)
Anti-cheating statement (2 points)
Five StatKey Pictures: ( 5 points each)
o Histogram (Picture of Histogram of your quantitative data with slider set to 5 bars)
o Summary Statistics (Picture of Summary Statistics for your quantitative data)
o Degrees of Freedom (Picture of Degrees of Freedom input box with correct degrees of freedom)
o Critical Value Graph (Picture of T – Distribution graph corresponding to correct degrees of
freedom and tail, 0.05 significance level in the top box, and critical value in bottom box.)
o P-value Graph (Picture of T – Distribution graph corresponding to correct degrees of freedom and
tail with the T – test statistic in the bottom box and P-value in top box).
Null and Alternative Hypotheses with correct symbolic notation and units (3 points each)
Sentence Explanations: Assumptions, Significance, Tail Explanations (3 points each)
T-test stat definition sentence, P-value definition sentence, Conclusion (4 points each)
All other problems: (2 points each)
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PROJECT REPORT DIRECTIONS: Use the quantitative column of data, population of interest, and claim
assigned to you by your instructor. You do not need to include the questions. Just provide the answers and
StatKey pictures requested for each number.
Put the following title and anti-cheating statement at the top of your report.
First and Last Name
Math 140 Project#4 One-Population Mean Hypothesis Test
Instructor’s Name
Section# for your class
Semester and Year
Cheating Statement: Confirm that you did not cheat. If true, write the following:
I did not cheat on this project. I did not copy someone else’s answers. I did the work myself. No one else
did this project for me.
Answer the following questions:
1.
What is the quantitative question?
2.
What is your population of interest?
3.
What is the claim about the population mean average that you are testing?
Math 140 PROJECT Directions and Grading Rubric
One-Population Mean Hypothesis T-Test
(Use with Teachout textbook Chapter 3)
Part II: Use your claim in #3 to write the Null Hypothesis and the Alternative Hypothesis.
4.
Write your null hypothesis using the population mean average symbol (µ) and symbol = , ≤ , or ≥
5.
Write your alternative hypothesis using the population mean average symbol (µ) and
symbol ≠ , > , or <
6.
Is the claim the null hypothesis ( ) or is the claim the alternative hypothesis ( ) ?
7.
Is your hypothesis test a “right-tailed test”, a “left-tailed test” or a “two-tailed test
Part III: Paste your column of quantitative data into StatKey, create a histogram and check the OnePopulation Mean T-test assumptions.
Open the Project Data Excel Spreadsheet. Highlight the column of numerical measurement data assigned to you,
right click and copy.
Go to www.lock5stat.com and click on StatKey. Click on ”One Quantitative Variable” under the “Descriptive Statistics
and Graphs” menu in StatKey.
Click on “Edit Data” and Copy and Paste your quantitative column of data into StatKey. If you have a title at the top,
Check the box for “header row”. If you do not have a title at the top, do NOT check the box that says header row.
Push OK.
Click on “Histogram” and change the number of buckets to 5. This will give you 5 bars in your histogram. Copy the
graph and the “Summary Statistics” next to the graph.
Put these StatKey Pictures on the Project Report:
8.
Copy and Paste a picture of the 5 bar histogram into your project report.
9.
Also copy and paste the “Summary Statistics” printout on the right of the histogram into your
project report. Make sure the table is large enough to read the numbers. If the table is too small, your
instructor will not be able to grade your report!
Example #8 & #9:
Math 140 PROJECT Directions and Grading Rubric
One-Population Mean Hypothesis T-Test
(Use with Teachout textbook Chapter 3)
Check the following three T-test conditions with your histogram and summary statistics from StatKey.
10. Condition #1: Was the sample data collected randomly or by a census? Explain why or why not.
11. Condition #2: Do you think the individual observations in your data are independent of each other
or are they related in some way. Explain why or why not.
12. Condition #3: What was the sample size? What is the shape of your data? Does your data have
either a normal (bell shaped) histogram OR a sample size of at least 30? Explain why or why not.
Part IV: Calculate your Degrees of Freedom, Standard Error, and the T – Test Statistic
13. What is your sample standard deviation ( s ) in your StatKey “Summary Statistics” table?
14. What is your sample size ( n ) in your StatKey “Summary Statistics” table?
15. Calculate the standard error for your data using the following formula and the answers to #14 and
#15. Be sure to show your work.
Standard Error =
=
√
Example: Standard Error = 7.245 ÷ √40 = 1.145535
16. What is the population mean average (µ) listed in the null hypothesis ( )? Example: Suppose the
null hypothesis is 10
� ) in your StatKey “Summary Statistics” table? Example: The
17. What is your sample mean average (
� ) in the StatKey Summary Statistics table is 13.150
sample mean average (
18. Calculate the T-test statistic using the following formula and the answers to #15, #16 and #17. Be
sure to show your work. Round your answer to the thousandths place. (3 numbers to the right of
decimal.) The T-test statistic may be negative or positive. Be sure to put the correct sign.
T – Test Statistic =
( − )
= ( ̅ − µ) ÷
Example: T – Test Statistic = (13.150 – 10) ÷ 1.145535 = +2.750
19. Write the definition sentence explaining the T – Test Statistic in context. If the T-test statistic in #17 is
positive, then the sample mean is this number of standard errors above the population mean in null
hypothesis. If the T-test statistic in #17 is negative, then the sample mean is this number of standard errors
below the population mean in null hypothesis.
Example: “The sample mean of 13.150 years was 2.750 standard errors above the
population mean of 10 years in the null hypothesis.”
Math 140 PROJECT Directions and Grading Rubric
One-Population Mean Hypothesis T-Test
(Use with Teachout textbook Chapter 3)
20. Calculate the Degrees of Freedom for your data using the formula (df = n – 1). “n” is your sample
size. Be sure to show your work.
Example: Degrees of Freedom = n – 1 = 40 – 1 = 39
Part V: Use StatKey and a 5% (0.05) Significance Level to calculate your Critical Value
21. Go to StatKey. Under “Theoretical Distributions”, click on “ t “. Enter the degrees of freedom you
listed in #20 into the df box and push OK. Take a picture of your degrees of freedom box.
Example:
22. Show the StatKey T-distribution Critical Value picture with correct degrees of freedom, 0.05
significance level and the correct tail for your alternative hypothesis.
Left Tail with df = 39 example (critical value -1.685):
Right Tail with df = 39 example (critical value +1.685):
Math 140 PROJECT Directions and Grading Rubric
One-Population Mean Hypothesis T-Test
(Use with Teachout textbook Chapter 3)
Two Tails with df = 39 example (notice 0.05 split into 0.025 in each tail, critical values -2.023 and +2.023):
23. What is your critical value or values? (This is where your tail or tails start.)
24. Look at your T – Test Statistic answer in #18 and tail with your critical value or values. Does your
T – Test Statistic fall in the tail or not? (If your test is two-tailed, does your T – Test Statistic fall in
either one of the tails or not?)
25. Does the sample mean significantly disagree with the population mean in the null hypothesis or
does the sample mean not significantly disagree with the population mean in the null hypothesis?
Explain why. (T-test stat in tail means the sample mean significantly disagree with the population mean
null hypothesis. T-test stat NOT in tail means the sample mean does NOT significantly disagree with
population mean in the null hypothesis)
Math 140 PROJECT Directions and Grading Rubric
One-Population Mean Hypothesis T-Test
(Use with Teachout textbook Chapter 3)
26. Does the sample data significantly disagree with the null hypothesis or does the sample data not
significantly disagree with the null hypothesis? Explain why. (T-test stat in tail means the sample data
significantly disagree with null hypothesis. T-test stat NOT in tail means the sample data does NOT
significantly disagree with null hypothesis.)
PART VI: Use StatKey and the T – Test Statistic to calculate the P-Value
27. Show the StatKey T-distribution P-value picture with correct degrees of freedom, the T-test statistic
from #18 in the bottom box, and the correct tail for your alternative hypothesis.
Left Tail with df = 39 and T-test statistic = +2.750 example (P-value = 0.996 = 99.6%):
Right Tail with df = 39 and T-test statistic = +2.750 example (P-value = 0.0045 = 0.45%):
Math 140 PROJECT Directions and Grading Rubric
One-Population Mean Hypothesis T-Test
(Use with Teachout textbook Chapter 3)
Two Tails with df = 39 and T-test statistic = +2.750 example (P-value = 0.0045 + 0.0045 = 0.009 = 0.9%):
28. What is your P-value? Write your P-value as a decimal proportion AND as a percentage.
29. Write the P-value definition sentence in context to explain your P-value.
Example: “If the null hypothesis is true and the population mean average lifespan of mammals is 10 years,
then there is a 0.45% probability of getting this sample data or more extreme by sampling variability.”
30. Is your P-value lower or higher than your 5% significance level? Is your P-value low or high?
(If the P-value is lower than the 5% significance level, it is considered a Low P-value. If the P-value is higher
than the 5% significance level, it is considered a High P-value. If a P-value was exactly 5%, that would be
considered a low P-value.)
31. If the null hypothesis was true, could the sample data have occurred because of sampling variability
or is it unlikely to be sampling variability? (Low P-value indicates that the data is unlikely to have
occurred because of sampling variability. High P-value indicates that the data could have occurred because
of sampling variability.)
32. Did your data pass all three of the T-test conditions in #10, #11 and #12?
33. Considering the assumptions, is your P-value significant evidence or not significant evidence? If the
P-value is low and the data passed all the conditions, the P-value is considered significant evidence. If the
P-value is low and the data did NOT pass all one or more of the conditions, then the P-value is NOT
significant evidence. A high P-value (with or without passing conditions) is NOT significant.)
Math 140 PROJECT Directions and Grading Rubric
One-Population Mean Hypothesis T-Test
(Use with Teachout textbook Chapter 3)
PART VII: Interpretations and Final Conclusion
34. Considering the assumptions and P-value, should we Reject the Null Hypothesis or Fail to reject the
Null Hypothesis? If the P-value is low and the data passed all the conditions, then you should REJECT the
NULL HYPOTHESIS. If the P-value is low and the data did NOT pass all of the assumptions, then you
should FAIL TO REJECT THE NULL HYPOTHESIS. A high P-value (with or without conditions) always
indicates that you should FAIL TO REJECT THE NULL HYPOTHESIS.
35. Write the standard conclusion sentence in context for your test addressing evidence, assumptions
and the claim in context. Here is an example sentence. You have to pick between “significant evidence”
or “not significant evidence”, “reject” or “support”, depending on your P-value, passing or failing the
assumptions, and if your claim is the null or alternative hypothesis.
Conclusion: There (is or is not) significant evidence to (reject or support) the claim that the population
mean average…
Remember use “reject” in your sentence if Ho was your claim in #6. Use “support” if Ha was your claim in
#6. If your P-value was higher than the 5% significance level or if the data did not pass ALL of the
assumptions, then you should say there is “not significant evidence”. Only if your P-value is lower than the
significance level AND your data passed all the assumptions, then you can say there “is significant
evidence”. Don’t forget to describe your claim in context.
Example: There is significant evidence to SUPPORT the claim that the population mean lifespan of
mammals is more than 10 years.
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