Researchers collected two different samples, X and Y, of temperatures, in degrees Celsius, of the habitat for Florida scrub lizards. The confidence interval 36±1.66 was constructed from sample X, and the confidence interval 36±1.08 was constructed from sample Y. Assume both samples had the same standard deviation.

Which of the following statements could explain why the width of the confidence interval constructed from X is greater than the width of the confidence interval constructed from Y?

A. The sample size of X is greater than the sample size of Y, and the confidence level is the same for both intervals.
B. The sample size of X is greater than the sample size of Y, and the confidence level used for the interval constructed from X is less than the confidence level used for the interval constructed from Y.
C. The sample size is the same for X and Y, and the confidence level used for the interval constructed from X is less than the confidence level used for the interval constructed from Y.
D. The sample size is the same for X and Y, and the confidence level is the same for both intervals.
E. The sample size is the same for X and Y, and the confidence level used for the interval constructed from X is greater than the confidence level used for the interval constructed from Y

Question

07-05-2020
Mathematics

contestada

Researchers collected two different samples, X and Y, of temperatures, in degrees Celsius, of the habitat for Florida scrub lizards. The confidence interval 36±1.66 was constructed from sample X, and the confidence interval 36±1.08 was constructed from sample Y. Assume both samples had the same standard deviation.

Which of the following statements could explain why the width of the confidence interval constructed from X is greater than the width of the confidence interval constructed from Y?

A. The sample size of X is greater than the sample size of Y, and the confidence level is the same for both intervals.
B. The sample size of X is greater than the sample size of Y, and the confidence level used for the interval constructed from X is less than the confidence level used for the interval constructed from Y.
C. The sample size is the same for X and Y, and the confidence level used for the interval constructed from X is less than the confidence level used for the interval constructed from Y.
D. The sample size is the same for X and Y, and the confidence level is the same for both intervals.
E. The sample size is the same for X and Y, and the confidence level used for the interval constructed from X is greater than the confidence level used for the interval constructed from Y

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kendrich kendrich · Answer 1 · 2020-05-11T14:56:57+02:00

Answer:

E. The sample size is the same for X and Y, and the confidence level used for the interval constructed from X is greater than the confidence level used for the interval constructed from Y

Step-by-step explanation:

Confidence interval formula is given as

CI = \bar{x} \pm z*(\sigma/\sqrt{n})

Here, we can see that the width of confidence interval is z*(\sigma/\sqrt{n}) , which is dependent only on z critical value, standard deviation (sigma) and sample size (n)

This simply entails that either z or n or both are greater for x as compared to y.

Option E is correct answer because x and y can have sample sizes, but if the z critical is greater for x, then the width will be larger.

priyankatutor priyankatutor · Answer 2 · 2022-01-17T12:19:42+01:00

The confidence interval tells about the probability where a value falls between a range. The interval constructed from X is greater than that of Y because the z value for X is greater than Y.

The confidence interval:

[tex]CI = \bar{x} \pm z\times (\dfrac {\sigma}{\sqrt{n}})[/tex]

Where,

[tex]CI[/tex] = confidence interval

[tex]\bar{x}[/tex] = sample mean

[tex]z[/tex] = confidence level value

[tex]{s}[/tex] = sample standard deviation

[tex]{n}[/tex] = sample size

From the formula, confidence interval is the the directly proportional to the confidence level value, standard deviation, and population.

Since the standard deviation, and the population is constant,

Therefore, the interval constructed from X is greater than that of Y because the z value for X is greater than Y.

Learn more about The confidence interval:

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