Dropbox Assignment 3
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Date
Feb 20, 2024
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Shaun Scott Math 250 BDE- Statistics I December 3
rd
2023
Dropbox Assignment 3
Question 1: According to a 2021 Gallup Poll, 428 out of 823 randomly selected adults living in the United States felt the laws covering the sale of firearms should be stricter. Find the 95% confidence interval. Assume that the conditions for using the CLT are met. Paste the results in your Word document and interpret the confidence interval.
Number of adults who feel laws should be stricter (
x
): 428
Total number of adults sampled (
n
): 823
Sample proportion (
p
^): x
n
P=
428
823
For a 95% confidence interval, the Z value is approximately 1.96.
Margin of Error
P=
428
823
= 0.5201
1.96
x
=
√
0.5201
∗(
1
−
0.5201
)
823
= 0.0366
Confidence Interval=0.5201±0.0366
Question 2: Do the 50 outcomes in the short run of flips in this data set suggest the coin is unfair? Open the provided dataset (you will need to have StatCrunch open before you click on the provided link) and perform the following:
Conduct a Hypothesis test using:
H0: p = .5
Ha: p ≠ .5
One sample proportion summary hypothesis test:
p: Proportion of successes
H
0
: p = 0.5
H
A
: p ≠ 0.5
Hypothesis test results:
ProportionCountTotalSample Prop.Std. Err.
Z-Stat
P-value
p
31
50
0.62
0.0707106781.69705630.0897
Calculate the test statistic and the p-value for a hypothesis test. Paste the results in your Word document.
Question 3: Do the 50 outcomes in the short run of flips in this data set suggest the coin is unfair? Using the same data from question 3, you can also find a 95% confidence interval showing the proportion of heads. Paste the results in your Word document. Interpret the confidence interval.
One sample proportion summary confidence interval:
p: Proportion of successes
Method: Standard-Wald
95% confidence interval results:
ProportionCountTotalSample Prop.Std. Err.
L. Limit
U. Limit
p
31
50
0.62
0.0686440090.485460210.75453979
Question 4: Are Americans Concerned About Global Warming? Confidence intervals can be used to think about questions like this. A 2021 Gallup poll found that 2256 out of 5127 Americans think that global warming will pose serious risk in the future. Provide answers to the following questions using complete sentences.
What percentage of Americans think that global warming will pose serious risk in the future?
Percentage= (
2256
5127
)= 0.44*100= 44.00%
Check the conditions to determine whether the CLT can be sued to find a confidence interval. Write on the conditions and explain/show that they have been met.
Randomization: The data should be collected from a random sample or randomized experiment. In this case, we assume that the Gallup poll used a random sampling method.
Independence: The sample size should be less than 10% of the population. With over 300 million
people in the U.S., a sample size of 5127 is less than 10%, so this condition is met.
Sample size/skew: we have 2256 "successes" (people who think global warming will pose a serious risk) and 2871 "failures" (people who don't), so this condition is met.
Find the 95% confidence interval for the population proportion of Americans that think that global warming will pose serious risk in the future. Copy the results into your Word document.
0.4401−1.96*
√
0.4401
∗(
1
−
0.4401
)
5127
=
√
0.24641199
5127
∗
1.96
=
√
0.24641199
10,048.92
= 0.00004939825
Confidence Interval=0.4401±0.000049
Interpret the 95% confidence interval for the population proportion of Americans that think global warming will pose serious risk in the future.
We are 95% confident that the true proportion of Americans who believe global warming will pose a serious risk in the future is between 42
Can the confidence interval be used to conclude that a majority of Americans think that global Warming will pose serious risk in the future?
Yes, it can conclude that a majority of Americans think that global Warming will pose serious risk in the future
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