SOLUTION: MAT 118 A1 Business and Technical College Statistics Worksheet

QUESTION 1
STATE THE RESEARCH QUESTION FOR THIS STUDY?
2 POINTS
QUESTION 2
WHO OR WHAT ARE THE OBSERVATIONAL UNITS IN THIS SCENARIO?
2 POINTS
QUESTION 3
IS THIS AN EXPERIMENT OR AN OBSERVATIONAL STUDY? EXPLAIN YOUR REASONING.
3 POINTS
QUESTION 4
STATE THE EXPLANATORY VARIABLE BEING MEASURED ON EACH OBSERVATIONAL
UNIT.
2 POINTS
QUESTION 5
STATE THE RESPONSE VARIABLE BEING MEASURED ON EACH OBSERVATIONAL UNIT.
2 POINTS
QUESTION 6
USING THE CORR/REGRESSION APPLET AND THE HANDSPAN DATA, CREATE A
SCATTERPLOT AND DESCRIBE THE ASSOCIATION BASED ON THE SCATTERPLOT. BE
SURE TO STATE THE DIRECTION, FORM, STRENGTH, AND STATE ANY OBSERVATIONS
THAT APPEAR TO BE UNUSUAL (OR STATE THAT THERE ARE NONE).
4 POINTS
QUESTION 7
STATE THE VALUE OF R FOR THIS SAMPLE. ALSO, DOES THE VALUE OF R MATCH THE
DESCRIPTION OF THE SCATTERPLOT FROM THE PREVIOUS QUESTION. EXPLAIN WHY
OR WHY NOT?
4 POINTS
QUESTION 8
STATE THE NULL AND ALTERNATIVE HYPOTHESIS TO BE TESTED IN THIS STUDY
USING THE CORRELATION. USE EITHER WORDS OR SYMBOLS.
4 POINTS
QUESTION 9
USING THE CORR/REGRESSION APPLET TO TEST YOUR HYPOTHESES FROM THE
PREVIOUS QUESTION USING SIMULATION BASED METHODS. REPORT THE P-VALUE
FROM YOUR SIMULATION AND STATE HOW MUCH EVIDENCE THERE IS AGAINST THE
NULL HYPOTHESIS
4 POINTS
QUESTION 10
USING THE CORR/REGRESSION APPLET, STATE THE EQUATION OF THE LINEAR
REGRESSION LINE.
1 POINTS
QUESTION 11
INTERPRET THE SLOPE OF THE REGRESSION LINE IN THE CONTEXT OF THE
PROBLEM.
4 POINTS
QUESTION 12
EITHER INTERPRET THE Y-INTERCEPT IN THE CONTEXT OF THE PROBLEM OR
EXPLAIN WHY IT HAS NO PRACTICAL MEANING.
3 POINTS
QUESTION 13
BASED ON THE LEAST-SQUARES REGRESSION EQUATION, PREDICT TO TWO DECIMAL
PLACES THE NUMBER OF TOOTSIE ROLLS A PERSON WITH A HAND SPAN OF 20 CM
CAN GRAB, ON AVERAGE.
4 POINTS
QUESTION 14
STATE THE VALUE OF R2 AND INTERPRET THAT VALUE IN THE CONTEXT OF THE
PROBLEM
4 POINTS
QUESTION 15
USING THE CORR/REGRESSION APPLET, CONDUCT A THEORY BASED HYPOTHESIS
TEST OF THE SLOPE BASED ON YOUR RESEARCH QUESTION. BE SURE TO STATE THE
NULL AND ALTERNATIVE HYPOTHESES, THE T-STATISTIC, THE P-VALUE, AND THE
STRENGTH OF EVIDENCE AGAINST THE NULL HYPOTHESIS.
8 POINTS
QUESTION 16
ARE YOU ABLE TO CONCLUDE THAT THE ASSOCIATION BETWEEN HAND SPAN AND
THE NUMBER OF TOOTSIE ROLLS GRABBED IS CAUSAL (DUE TO CAUSE AND EFFECT).
WHY OR WHY NOT?
3 POINTS
QUESTION 17
ARE YOU ABLE TO GENERALIZE THESE RESULTS TO A LARGER POPULATION? WHY OR
WHY NOT?
3 POINTS
QUESTION 18
SUMMARIZE THE RESULTS OF THE STUDY. WRITE AT LEAST A SENTENCE OR TWO
ABOUT WHAT YOU WOULD CONCLUDE BASED ON THE WORK YOU’VE DONE IN THE
PREVIOUS QUESTIONS.
5 POINTS
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INVESTIGATION: ASSOCIATION BETWEEN
HAND SPAN AND CANDY?
Is hand span a good predictor of how much candy you can grab? Using 45 college students as
subjects, researchers set out to explore whether a linear relationship exists between hand span
(cm) and the number of Tootsie Rolls each subject could grab.
STEP 1: Ask a research question.
590
1. State the research question.
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STEP 2: Design a study and collect data.
2. What are the observational/experimental units?
3. Is this a randomized experiment or an observational study? Explain how you know.
4. State the two variables measured on each unit.
5. Is there an explanatory/response relationship for these variables? Classify the variables in
this study as categorical or quantitative.
6. State the null and alternative hypotheses to be investigated with this study.
STEP 3: Explore the data.
7. Use the data set HandSpan to calculate means, standard deviations, and the correlation
coefficient.
8. Create a scatterplot of the data with hand span on the x-axis and number of Tootsie Rolls
on the y-axis.
9. Does there appear to be an association between hand span and number of Tootsie Rolls?
Describe the direction, form, and strength of the association: Is it positive, negative, weak,
strong, linear?
10. Are there any unusual observations?
11. Find the least squares regression equation that predicts number of Tootsie Rolls based on
hand span.
12. Interpret the slope of the least squares regression equation in terms of hand span and
predicted number of Tootsie Rolls grabbed.
STEP 4: Draw inferences.
13. Use the appropriate applet to construct a simulated null distribution using the slope of the
least squares regression line as the statistic. Mark the observed least squares slope on this
graph.
a. Paste a screenshot or draw your null distribution below with the observed slope marked
and the approximate p-value shaded in.
b. Is the observed statistic out in the tail of this null distribution or is it a fairly typical
result?
c. What is the p-value from your simulation? Based on this simulation analysis, would
you conclude that the data provide strong evidence against the null hypothesis and con-
clude that there is a significant association between hand span and number of Tootsie
Rolls grabbed? Explain your reasoning.
14. Are the validity conditions met to complete a theory-based t-test on these data? Explain.
Whether the conditions are met or not, use a theory-based t-test to find a p-value. How
does this p-value compare to the p-value your found using the randomization method?
15. Find a confidence interval for the slope that would describe the association between all
hand spans and number of Tootsie Rolls grabbed. Is zero in this interval? Does this make
sense based on the p-value from your test of significance?
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STEP 5: Formulate conclusions.
16. Are you able to conclude that the association between hand span and number of Tootsie
Rolls grabbed is causal? Explain.
17. What generalizations are you willing to make? Explain.
STEP 6: Look back and ahead.
18. Summarize the findings from the study. What worked well in this study design? What
would you change? What are some follow-up research questions you would like to explore
based on the findings from this study?
(3)
Research Article
www.wiley.com/college/tintle
Music Problems Read “Early Adolescent Music Preferences and Minor Deliquency by
ter Bogt, Keijsers, Meeus, et al. (2013), 131(2), 1-10, in the Journal of Pediatrics.

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