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cookiemonster0476
24.03.2020 •
Mathematics
Suppose that on a 100-point test, the goal is for the students' exam scores to have a standard deviation of less than 10 pts. A recent sample of 22 exams has a standard deviation of 12.1. Use alpha = 0.05.
H0: population variance > or = 100
H1: population variance < 100
What is the critical Chi-square value?
For the same hypothesis test, what is the Chi-Square statistic?
For the same hypothesis test, what is the p-Value?
For the same hypothesis test, interpret the results.
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Ответ:
a) chi square test value = 32.2
b) The tabulated value 32.671 at α =0.05 level of significance
c) conclusion:-
null hypothesis is accepted
population variance is greater than or equal to 100
Step-by-step explanation:
Step1:-
Given size of the sample 'n' = 22 and standard deviation 'S'= 12.1
H0: population variance > or = 100
H1: population variance < 100
level of significance,
=0.05
By using chi square test χ^2 = ∑
=
And another formula is χ^2 =![\frac{nS^2}{variance}](/tpl/images/0560/1768/0aec9.png)
'S' be the sample standard deviation = 12.1
Given size of the sample 'n' = 22
Step 2:-
By using chi square test![χ^2 =\frac{nS^2}{б^2}](/tpl/images/0560/1768/fd127.png)
substitute all given values
now chi square test =![\frac{22(12.1)^{2} }{100} = \frac{3221.02}{100} = 32.2](/tpl/images/0560/1768/db4dd.png)
calculated chi square test = 32.2
The degrees of freedom = n-1 in chi-square distribution
The degrees of freedom = 22-1 =21 at 5% level of significance
The tabulated value from chi square table = 32.671
calculated chi square test = 32.2< The tabulated value 32.671
so the null hypothesis is accepted
Therefore population variance is greater than or equal to 100
Conclusion
a) chi square test value = 32.2
b) The tabulated value 32.671 at α =0.05 level of significance
c) conclusion:-
null hypothesis is accepted
population variance is greater than or equal to 100
Ответ: