Assuming that the population is normally distributed, construct a 95% confidence interval for the population mean for each of the samples below. Explain why these two samples produce different confidence intervals even though they have the same mean and range. Sample A 1, 3,3,3,6,6,6,8 Sample B 1,2,3,4,5,6,7,8 Construct a 95% confidence interval for the population mean for sample A. ---≤µ≤---- enter your response here (Type integers or decimals rounded to two decimal places as needed.) Part 2 Construct a 95% confidence interval for the population mean for sample B. --≤µ≤--- enter your response here (Type integers or decimals rounded to two decimal places as needed.) Part 3 Explain why these two samples produce different confidence intervals even though they have the same mean and range. A. The samples produce different confidence intervals because their standard deviations are different. B. The samples produce different confidence intervals because their medians are different. C. The samples produce different confidence intervals because their critical values are different. D. The samples produce different confidence intervals because their sample sizes are different.

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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Assuming that the population is normally distributed, construct a 95% confidence interval for the population mean for each of the samples below. Explain why these two samples produce different confidence intervals even though they have the same mean and range.

Sample A 1, 3,3,3,6,6,6,8

Sample B 1,2,3,4,5,6,7,8

Construct a 95% confidence interval for the population mean for sample A.

---≤µ≤----

enter your response here (Type integers or decimals rounded to two decimal places as needed.)

Part 2 Construct a 95% confidence interval for the population mean for sample B.

--≤µ≤---

enter your response here (Type integers or decimals rounded to two decimal places as needed.)

Part 3 Explain why these two samples produce different confidence intervals even though they have the same mean and range.

A. The samples produce different confidence intervals because their standard deviations are different.

B. The samples produce different confidence intervals because their medians are different.

C. The samples produce different confidence intervals because their critical values are different.

D. The samples produce different confidence intervals because their sample sizes are different.

Definition Definition Middle value of a data set. The median divides a data set into two halves, and it also called the 50th percentile. The median is much less affected by outliers and skewed data than the mean. If the number of elements in a dataset is odd, then the middlemost element of the data arranged in ascending or descending order is the median. If the number of elements in the dataset is even, the average of the two central elements of the arranged data is the median of the set. For example, if a dataset has five items—12, 13, 21, 27, 31—the median is the third item in ascending order, or 21. If a dataset has six items—12, 13, 21, 27, 31, 33—the median is the average of the third (21) and fourth (27) items. It is calculated as follows: (21 + 27) / 2 = 24.

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