Assuming that the population is normally distributed, construct a 90% confidence interval for the population mean, based on the following sample size of n=5. 1, 2, 3, 4, and 23 In the given data, replace the value 23 with 5 and recalculate the confidence interval. Using these results, describe the effect of an outlier (that is, an extreme value) on the confidence interval, in general. Find a 90% confidence interval for the population mean, using the formula or technology. ?≤μ≤? (Round to two decimal places as needed.) In the given data, replace the value 23 with 5. Find a 90% confidence interval for the population mean, using the formula or technology. ?≤μ≤? (Round to two decimal places as needed.) Using the results from the previous two steps, what is the effect of an outlier (that is, an extreme value) on the confidence interval, in general? A. The presence of an outlier in the original data increases the value of the sample mean and greatly inflates the sample standard deviation, widening the confidence interval. B. The presence of an outlier in the original data decreases the value of the sample mean and greatly decreases the sample standard deviation, narrowing the confidence interval. C. The presence of an outlier in the original data decreases the value of the sample mean and greatly inflates the sample standard deviation, widening the confidence interval. D. The presence of an outlier in the original data increases the value of the sample mean and greatly decreases the sample standard deviation, narrowing the confidence interval.

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

90%

confidence interval for the population mean, based on the following sample size of n=5.

1, 2, 3,

and

In the given data, replace the value

with

and recalculate the confidence interval. Using these results, describe the effect of an outlier (that is, an extreme value) on the confidence interval, in general.

Find a

90%

confidence interval for the population mean, using the formula or technology.

?≤μ≤?

(Round to two decimal places as needed.)

In the given data, replace the value

with

Find a

90%

confidence interval for the population mean, using the formula or technology.

?≤μ≤?

(Round to two decimal places as needed.)

Using the results from the previous two steps, what is the effect of an outlier (that is, an extreme value) on the confidence interval, in general?

The presence of an outlier in the original data increases the value of the sample mean and greatly inflates the sample standard deviation, widening the confidence interval.

The presence of an outlier in the original data decreases the value of the sample mean and greatly decreases the sample standard deviation, narrowing the confidence interval.

The presence of an outlier in the original data decreases the value of the sample mean and greatly inflates the sample standard deviation, widening the confidence interval.

The presence of an outlier in the original data increases the value of the sample mean and greatly decreases the sample standard deviation, narrowing the confidence interval.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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