MATH 128 Joliet Junior College Statistics Worksheet

MATH128 Exam 2 Spring 2020Name:
Answer all questions. Answers without justification may not receive full credit.
1. Janine is a volleyball player who is practicing her short serves because her team is in an upcoming
match against an opponent who does not return short serves very well. Janine must land a majority
of her short serves in bounds or her coach will not let her use her short serve in the upcoming match.
Janine short serves 30 times and lands 20 in bounds. The coach wants to determine if Janine is more
likely to land her short serves inbounds. Answer the following questions using this information.
(a) What is the research question? Write it in the form of a QUESTION.
(b) Answer all the following questions:
1. What is the sample size?
2. What are the observational units?
3. What is the variable?
4. What type of variable is it?
(c) Describe the null hypothesis and alternative hypotheses without referring to a parameter value.
1. Null:
2. Alternative:
(d) Write the null hypothesis and alternative hypothesis in correct notation and symbols.
(e) Could the researchers use the theory-based approach on this study? Explain clearly why or why
not.
Janine’s coach ran a simulation using the one-proportion applet with the following results. Answer the remaining questions (e)-(m) using this information.
(f) State the following values from the simulation.
1. Mean simulated p̂ =
2. SD of p̂ =
3. p-value =
(g) Calculate the value of Z using the simulation. Round to two decimal places.
(h) Interpret the value of Z in terms of distance. Do not refer to any conclusions concerning strength
of evidence, etc.
(i) Interpret the p-value in terms of probability. Do NOT refer to any conclusions concerning
strength of evidence.
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(j) Using the p-value and the guidelines for evaluating strength of evidence, which of the following
is correct?
A. little to no evidence against the null hypothesis
B. moderate evidence against the null hypothesis
C. strong evidence against the null hypothesis
D. very strong evidence against the null hypothesis
(k) Using the Z-score and the guidelines for evaluating strength of evidence, which of the following
is correct?
A. little to no evidence against the null hypothesis
B. moderate evidence against the null hypothesis
C. strong evidence against the null hypothesis
D. very strong evidence against the null hypothesis
(l) Use your p-value results to select all of the following statements which are correct. There may
be one, none, or several correct. Please read the options carefully and select all that are true.
A. The results are unlikely if the null is true.
B. The null is not a believable or reasonable explanation for our observed results.
C. The results are not statistically significant.
D. The researchers have proven that the null is false.
E. The researchers have proven that the null is true.
(m) Write a one-sentence accurate summary of the results without referring to any statistical jargon.
Write the sentence as if you are writing to someone who does not know anything about statistics.
Your sentence should include the context of the study.
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2. Emma, Nathan, Charles, and Hudson conduct a statistical study where
H0 : π = 0.60 vs HA : π 6= 0.60
and all four use a sample size of 128 and with same SE. However, all four get different values of p̂
according to the following table.
Researcher
p̂
Emma
0.48
Nathan
0.91
Charles
0.85
Hudson
0.24
(a) Which researcher will have the smallest p-value?
A. Nathan
B. Emma
C. Charlie
D. Hudson
(b) Which researcher will have the weakest evidence against the null?
A. Nathan
B. Emma
C. Charlie
D. Hudson
(c) Which researcher will have the largest |Z|?
A. Emma
B. Charles
C. Nathan
D. Not enough information to determine.
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3. Emma, Nathan, Charles, and Hudson conduct the same statistical study but each uses a different
sample size. Each calculated the same value of p̂.
Researcher
Emma
Nathan
Charles
Hudson
Sample Size
123
87
137
64
Answer the following questions based on this information.
(a) Which of the following researchers will have the smallest SE?
A. Emma
B. Nathan
C. Hudson
(b) Which of the following researchers will have the smallest p-value?
A. Hudson
B. Nathan
C. Emma
(c) Which of the following researchers will have the smallest |Z|?
A. Emma
B. Charles
C. Nathan
(d) Which researcher will have the weakest evidence against the null?
A. Hudson
B. Emma
C. Nathan
D. Charles
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Formulas and guidelines:
(a) Z =
p̂ − π
for simulation
SE
p̂ − π
(b) Z =
for the theory-based approach where σp̂ =
σp̂
(c)
(d)
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r
π(1 − π)
n