BFW Publishers An article in Forbes magazine claims that half of the adults in the United States do not have any savings. To substantiate that claim, the company, GoBanking, asked a random sample of 500 adults around the country how much money they have in savings and found that 265, or 53% of them, had no savings. To determine if these data provide convincing evidence that more than half of the adults in the United States do not have any savings, 200 simulated SRSS were selected. Each dot in the graph shows the number of adults that have no savings in a simulated SRS of 500 adults, assuming that each person has a 50% chance of not having any savings. The sample result showed that 265 out of 500 adults had no savings. The simulation shows the number of adults out of 500 that we can expect to have no savings if 50% is true.
BFW Publishers An article in Forbes magazine claims that half of the adults in the United States do not have any savings. To substantiate that claim, the company, GoBanking, asked a random sample of 500 adults around the country how much money they have in savings and found that 265, or 53% of them, had no savings. To determine if these data provide convincing evidence that more than half of the adults in the United States do not have any savings, 200 simulated SRSS were selected. Each dot in the graph shows the number of adults that have no savings in a simulated SRS of 500 adults, assuming that each person has a 50% chance of not having any savings. The sample result showed that 265 out of 500 adults had no savings. The simulation shows the number of adults out of 500 that we can expect to have no savings if 50% is true.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:BFW Publishers
An article in Forbes magazine claims that half of the adults in the United States do not have any savings. To substantiate that
claim, the company, GoBanking, asked a random sample of 500 adults around the country how much money they have in
savings and found that 265, or 53% of them, had no savings.
To determine if these data provide convincing evidence that more than half of the adults in the United States do not have any
savings, 200 simulated SRSS were selected. Each dot in the graph shows the number of adults that have no savings in a
simulated SRS of 500 adults, assuming that each person has a 50% chance of not having any savings. The sample result showed
that 265 out of 500 adults had no savings. The simulation shows the number of adults out of 500 that we can expect to have no
savings if 50% is true.
220 225 230 235 240 245 250 255 260 265 270 275 280
Simulated sample count of adults that do not have any savings
Based on the results of the simulation, is there
convincing evidence that at least 50% of adults do not
have any savings?
Yes, based on the simulation, only 2 of the
simulated samples show 265 out of 500 adults that
have no savings. This is highly unlikely, and
therefore provides convincing evidence that at least
50% of adults do not have any savings.
No, based on the simulation, 12% of the simulated
samples show 265 or more out of 500 adults have no
savings. Because it is not surprising to get a sample
count of 265 or more out of 500 when the
population proportion is 50%, we do not have
convincing evidence that at least 50% of adults do
not have any savings.
No, the simulation is centered near 250, which is
50% of 500, just as claimed by Forbes magazine.
This means that there is not convincing evidence
that at least 50% of adults do not have any savings.
Yes, based on the simulation, 12% of the simulated
samples show 265 or more out of 500 adults have no
savings. Because it is surprising to get a sample
count of 265 or more out of 500 when the
population proportion is 50%, we have convincing
evidence that at least 50% of adults do not have any
savings.
Yes, the simulation is centered near 250, which is
50% of 500, just as claimed by Forbes magazine.
This provides convincing evidence that at least 50%
of adults do not have any savings.
Expert Solution
Step 1
Given claim: At least 50% of the adults do not have any savings.
Null Hypothesis:
H0: At least 50% of the adults do not have any savings
Alternative Hypothesis:
H1: Less than 50% of the adults do not have any savings.
Given information:
The sample result showed 265 out of 500 adults had no savings.
There are 200 simulated samples are there.
Decision Rule:
If the proportion value of simulated sample of more than 265 is less than 0.05, reject the null hypothesis.
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