One Sample Hypothesis testing Worksheet #1 (SP2024) - edited
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Johnson County Community College *
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181
Subject
Mathematics
Date
Apr 3, 2024
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3
Uploaded by GrandWater13233
One-Sample Hypothesis Testing Worksheet #1 Name_____________________________________ Math 181 Statistics
Helgeson Due at the start of class
on Wednesday
, March 20, 2024. 1.
From looking at Helgeson’s red & white bead container that does not have the red and white beads all mixed together, but rather, has the red and white beads separated from each other, it appears
that the percentage of red beads in the container may be less than 50%. Perform a one-sided theory-based hypothesis test using the ˆ
p
from among your three sample proportions that is the smallest (and should be less than 0.5) in order to see if this sample of yours is providing strong enough evidence for you to conclude that the actual population proportion of red beads in the container of 6000 red & white beads is less than 50%. You do not have to verify the Central Limit Theorem validity conditions here since this verification was already completed in problem 2 (c) on the Sections 2.1 & 2.2 Bead data Worksheet that was due on Wednesday, March 6, 2024. Using words: (a)
:
o
H
the actual proportion of red beads in Helgeson’s container of 6000 red & white beads is 50% :
a
H
Using symbols: (b)
:
0.5
o
H
π
=
:
a
H
(c)
What is your observed statistic? In other words, what is the ˆ
p
that you are using? (Give your answer as both a fraction and a decimal rounded to 4 decimal places.) (d)
What is the theory-based standardized statistic? z
= (e)
What is the p-value? And what is your decision based on the strength of your evidence? Circle one: Reject o
H
/
Fail to Reject o
H
(f)
What is your conclusion in context?
2 2.
Suppose there is an election being held this week. Let’s suppose that in one congressional district in Kansas with over 50,000 registered voters there are two candidates competing against each other and the candidates last names are Snyder and Williams. An exit poll is conducted of 1340 random voters in this congressional district on election day. Each selected voter is asked who they voted for, Snyder or Williams, when they exit their polling place. Here are the results from the exit poll: Snyder = 649 votes Williams = 691 votes (a)
What is the variable? (b)
Is the variable categorical and binary
or quantitative
? Since Williams received more votes in the exit poll, let’s choose “Success” to be voting for Williams. (c)
What is the observed statistic? (Label this statistic with the appropriate symbol.) (d)
What would be the alternative hypothesis for a one-sided test? :
o
H
Each candidate will receive 50% of the vote in the election :
a
H
(e)
Are the validity conditions met in this problem in order to do a theory-based test? (Show your verifications for all necessary validity conditions)
3 2.
(Continued) (f)
If your answer to part (e) is yes, what is the theory-based p-value and standardized statistic? (g)
Based on the strength of your evidence, would you be willing to call the election for Williams (who received more than 50% of the votes in the exit poll) during the evening of the election before all of the votes are counted? Explain why or why not using the strength of the evidence provided by the exit poll.
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