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Answer:
a. We are 90% sure that the mean GPA for all students at her school is between 3.14 and 3.52.
b. The length would increase.
c. The interval would be narrower.
d. The biggest potential source of bias is making the students state their grades aloud, which makes it possible that students with low grades could lie their grades, making it seem higher, and the interval biased.
Step-by-step explanation:
x% confidence interval:
A confidence interval is built from a sample, has bounds a and b, and has a confidence level of x%. It means that we are x% confident that the population mean is between a and b.
Margin of error of a confidence interval:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which z is related to the confidence level(higher the confidence level, higher z) [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
This shows that if we increase the confidence level, the margin of error gets larger and the interval gets wider, while if we increase the sample size the margin of error gets smaller and the interval gets narrower.
a. Interpret the confidence level.
We are 90% sure that the mean GPA for all students at her school is between 3.14 and 3.52.
b. Explain what would happen to the length of the interval if the confidence level were increased to 99%.
We would increase the confidence level, and the interval would get wider, that is, the length would increase.
c. How would a 90% confidence interval based on a sample of size 200 compare to the original 90% interval?
Larger sample size means that the interval would be narrower.
d. Describe one potential source of bias in Ellery's study that is not accounted for by the margin of error.
The biggest potential source of bias is making the students state their grades aloud, which makes it possible that students with low grades could lie their grades, making it seem higher, and the interval biased.
Based on the information given in the sample, it should be noted that this implies that we are 90% sure that the mean GPA for all students at the school is between 3.14 and 3.52.
Sampling
- The thing that will happen to the length of the interval if the confidence level were increased to 99% is that the length would increase.
- A 90% confidence interval based on a sample of size 200 compare to the original 90% interval is that the interval would be narrower.
Lastly, a potential source of bias in Ellery's study that is not accounted for by the margin of error is making the students state their grades aloud. This will make some of them with lower grades lie.
Learn more about sampling on:
https://brainly.com/question/17831271
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