Answered: To test H0: σ=1.4 versus H1: σ≠1.4, a…

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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Question

To test

H0: σ=1.4

versus

H1: σ≠1.4,

a random sample of size

n=21

is obtained from a population that is known to be normally distributed.

(a) If the sample standard deviation is determined to be

s=2.3,

compute the test statistic.

χ20=3.723.72

(Round to three decimal places as needed.)

(b) If the researcher decides to test this hypothesis at the

α=0.10

level of significance, determine the critical values.

The critical values are

χ20.05=nothing

and

χ20.95=nothing.

(Round to three decimal places as needed.)

A graph with unlabeled horizontal and vertical axes contains a chi-square distribution curve that rises from left to right at an increasing and then decreasing rate to a peak about one quarter of the way from the left edge of the graph and then falls from left to right at an increasing and then decreasing rate to the right edge of the graph. There are two vertical lines that extend from the horizontal axis to the curve. The leftmost line is to the left of the peak. The rightmost line is to the right of the peak. The region under the curve between the vertical lines is shaded.

A graph with unlabeled horizontal and vertical axes contains a chi-square distribution curve that rises from left to right at an increasing and then decreasing rate to a peak about one quarter of the way from the left edge of the graph, and then falls from left to right at an increasing and then decreasing rate to the right edge of the graph. There is one vertical line that extends from the horizontal axis to the curve and is to the right of the peak. The region under the curve to the right of the line is shaded.

A graph with unlabeled horizontal and vertical axes contains a chi-square distribution curve that rises from left to right at an increasing and then decreasing rate to a peak about one quarter of the way from the left edge of the graph and then falls from left to right at an increasing and then decreasing rate to the right edge of the graph. There are two vertical lines that extend from the horizontal axis to the curve. The leftmost line is to the left of the peak. The rightmost line is to the right of the peak. The regions under the curve between the vertical axis and the leftmost line and to the right of the rightmost line are shaded.

A graph with unlabeled horizontal and vertical axes contains a chi-square distribution curve that rises from left to right at an increasing and then decreasing rate to a peak about one quarter of the way from the left edge of the graph and then falls from left to right at an increasing and then decreasing rate to the right edge of the graph. There is one vertical line that extends from the horizontal axis to the curve and is to the left of the peak. The region under the curve between the vertical axis and the line is shaded.

(d) Will the researcher reject the null hypothesis? Why? Choose the correct answer below.

Yes,

because the test statistic

is not

in the critical region.

No,

because the test statistic

in the critical region.

Yes,

because the test statistic

in the critical region.

No,

because the test statistic

is not

in the critical region.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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