MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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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.)
​(c) Draw a​ chi-squared distribution and depict the critical region. Choose the correct graph below.
 
 
A.
 
 
 
 
 
 
 
  •  
  •  
  •  
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.
 
B.
 
 
 
 
 
 
  •  
  •  
  •  
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.
 
C.
 
 
 
 
 
 
 
 
  •  
  •  
  •  
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.
 
D.
 
 
 
 
 
 
  •  
  •  
  •  
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.
 
 
A.
Yes​,
because the test statistic
is not
in the critical region.
 
B.
No​,
because the test statistic
is
in the critical region.
 
C.
Yes​,
because the test statistic
is
in the critical region.
 
D.
No​,
because the test statistic
is not
in the critical region.
 
 
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