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Compute the standardized test statistic, x2, to test the claim…

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Compute the standardized test statistic...
Compute the standardized test statistic, x2, to test the claim: The known population s.d. less than or equal to 3.2 if n=20, s2=6.2, and a confindence level of 0.01
Submitted: 8 years ago.Category: Math Homework
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Answered in 17 minutes by:
6/25/2010
Math Tutor or Teacher: rajeevanpillai, Master's Degree replied 8 years ago
rajeevanpillai
rajeevanpillai, Master's Degree
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Null hypothesis H0: σ ≤ 3.2
Alternative hypothesis: σ > 3.2
n = 20
s^2 = 6.2

(n-1)*s^2 19*6.2 117.8
test statistic = Χ^2 = -------------- = -------------- = -------------- = 11.504
σ0^2 3.2^2 10.24

α = 0.01
Critical value of X^2 with 19 degrees of freedom = 36.191

The computed value of chi-square does not exceed the critical value.

So sufficient evidence is not available to reject the null hypothesis.

Conclusion: the claim cannot be rejected.
The population standard deviation is less than or equal to 3.2


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Customer reply replied 8 years ago

I have a multiple choice answer of 36.813...which seems close to your critical value.

 

I will actually list all answers:

 

9.322

12.82

36.813

33.41

 

Can you please help me further...I want to be sure.

Customer reply replied 8 years ago

Can you answer more questions for me? I am not sure if you have an answer for the 1st one already?

Math Tutor or Teacher: Stevewh, Bachelor's Degree replied 8 years ago
Stevewh
Stevewh, Bachelor's Degree
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Hi,

H0: σ^2≤3.2
Ha: σ^2>3.2

Test-statistic = (n-1)s^2/σ^2 = 19(6.2)/3.2=36.813

Answer: 36.813 (3rd option)

Bonus is appreciated

Thanks

Steve
Stevewh
Stevewh, Bachelor's Degree
Category: Math Homework
Satisfied Customers: 7,610
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