Answered: To test H0: σ=2.2 versus H1: σ>2.2, 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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To test

H0: σ=2.2

versus

H1: σ>2.2,

a random sample of size

n=17

is obtained from a population that is known to be normally distributed. Complete parts (a) through (d).

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

s=2.4,

compute the test statistic.

χ20=nothing

(Round to three decimal places as needed.)

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

α=0.01

level of significance, determine the critical value.

χ20.01=nothing

(Round to three decimal places as needed.)

3219.04

A graph has a horizontal axis with two labeled coordinates at 19.04 and 32 and an unlabeled vertical axis. The graph 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 at 19.04 and is to the right of the peak. The rightmost line is at 32 and is to the right of the peak. The region under the curve to the right of the rightmost line is shaded.

5.81232.000

A graph has a horizontal axis with two labeled coordinates at 5.812 and 32.000 and an unlabeled vertical axis. The graph 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 at 5.812 and is to the left of the peak. The rightmost line is at 32.000 and 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.

5.81232.000

A graph has a horizontal axis with two labeled coordinates at 5.812 and 32.000 and an unlabeled vertical axis. The graph 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 at 5.812 and is to the left of the peak. The rightmost line is at 32.000 and is to the right of the peak. The region under the curve between the vertical axis and the leftmost line is shaded.

3219.04

(d) Will the researcher reject the null hypothesis?

Do not reject

because

χ20<χ20.01.

Reject

because

χ20>χ20.01.

Do not reject

because

χ20>χ20.01.

Reject

because

χ20<χ20.01.

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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