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Statistics
Study Set
Introduction to Business Statistics
Quiz 13: Chi-Square Applications
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Question 121
Essay
A random sample of 5 observations was drawn from a normal population.These were: 18,16,10,13,and 23.Test the hypotheses: H
0
:
σ
2
≤
20
\sigma ^ { 2 } \leq 20
σ
2
≤
20
H
1
:
σ
2
>
20
\sigma ^ { 2 } > 20
σ
2
>
20
at the 10% significance level. Test statistic = ____________________ Critical Value = ____________________ Conclusion: ____________________ Interpretation: _________________________________________________
Question 122
Short Answer
A random sample of 5 observations was drawn from a normal population.These were: 18,16,10,13,and 23.Estimate the population variance with 90% confidence. Lower value = ____________________ Upper value = ____________________
Question 123
Essay
Hypotheses In testing the hypotheses: H
0
:
σ
2
=
0.01
\sigma ^ { 2 } = 0.01
σ
2
=
0.01
H
1
:
σ
2
≠
0.01
σ ^ { 2 } \neq 0.01
σ
2
=
0.01
a random sample of 10 observations was drawn from a normal population,and the sample standard deviation was 0.043. -Determine the rejection region at the 5% significance level.
Question 124
Short Answer
In order to examine whether a sample could have come from a given type of population distribution (e.g.,the normal distribution),chi-square analysis involves the comparison of a table of ______________________________ Oij with a table of ______________________________ Eij that has been constructed under the assumption that the null hypothesis is true.
Question 125
Essay
What is the rationale for df = (r - 1)(k - 1)in conducting a chi-square test of independence for a contingency table with r rows and k columns?
Question 126
Essay
A sample of size 20 is used to obtain the following statistics:
∑
x
i
=
4363
\sum x _ { i } = 4363
∑
x
i
=
4363
and
Σ
x
i
2
=
953
,
180
\Sigma \mathrm { x } _ { i } ^ { 2 } = 953,180
Σ
x
i
2
=
953
,
180
Can we conclude at the 1% significance level that the population variance is less than 100? Hypotheses: Test statistic = ____________________ Critical Value = ____________________ Conclusion: _________________________ Interpretation: __________________________________________________
Question 127
Essay
Hypotheses In testing the hypotheses: H
0
:
σ
2
=
0.01
\sigma ^ { 2 } = 0.01
σ
2
=
0.01
H
1
:
σ
2
≠
0.01
σ ^ { 2 } \neq 0.01
σ
2
=
0.01
a random sample of 10 observations was drawn from a normal population,and the sample standard deviation was 0.043. -What is the conclusion?
Question 128
Short Answer
In preparing a confidence level for a population variance,the size of the sample is 12,and the level of confidence is 0.90.What are the appropriate table values for this interval? ____________________ and ____________________