Mixing
variance validation
The scores on a placement test given to college
freshmen for the past five years are approximately normally
distributed with a mean $μ = 74$ and a variance
$σ^2 = 8$. Would you still consider $σ^2 = 8$ to be a valid
value of the variance if a random sample of $20$ students
who take the placement test this year obtain a value of
$s^2 = 20$?
I think I'm supposed to use the F-distribution somehow in this problem, however, I've only been able to find out how to compare to sample variances--not how to compare a sample variance with a population variance. Any tips on how to solve this?
statistics
asked Feb 9 '15 at 3:21
hildk
11
add a comment |
The scores on a placement test given to college
freshmen for the past five years are approximately normally
distributed with a mean $μ = 74$ and a variance
$σ^2 = 8$. Would you still consider $σ^2 = 8$ to be a valid
value of the variance if a random sample of $20$ students
who take the placement test this year obtain a value of
$s^2 = 20$?
I think I'm supposed to use the F-distribution somehow in this problem, however, I've only been able to find out how to compare to sample variances--not how to compare a sample variance with a population variance. Any tips on how to solve this?
statistics
asked Feb 9 '15 at 3:21
hildk
11
add a comment |
The scores on a placement test given to college
freshmen for the past five years are approximately normally
distributed with a mean $μ = 74$ and a variance
$σ^2 = 8$. Would you still consider $σ^2 = 8$ to be a valid
value of the variance if a random sample of $20$ students
who take the placement test this year obtain a value of
$s^2 = 20$?
I think I'm supposed to use the F-distribution somehow in this problem, however, I've only been able to find out how to compare to sample variances--not how to compare a sample variance with a population variance. Any tips on how to solve this?
statistics
asked Feb 9 '15 at 3:21
hildk
11
The scores on a placement test given to college
freshmen for the past five years are approximately normally
distributed with a mean $μ = 74$ and a variance
$σ^2 = 8$. Would you still consider $σ^2 = 8$ to be a valid
value of the variance if a random sample of $20$ students
who take the placement test this year obtain a value of
$s^2 = 20$?
I think I'm supposed to use the F-distribution somehow in this problem, however, I've only been able to find out how to compare to sample variances--not how to compare a sample variance with a population variance. Any tips on how to solve this?
statistics
statistics
asked Feb 9 '15 at 3:21
hildk
11
asked Feb 9 '15 at 3:21
hildk
11
asked Feb 9 '15 at 3:21
hildk
11
asked Feb 9 '15 at 3:21
hildk
11
asked Feb 9 '15 at 3:21
hildk
11
11
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
Hypotheses:
$H_0: sigma^2 = 8$
$H_1: sigma^2 neq 8$
This is a $chi^2$ test for one variance problem.
Assumptions (taken from Statistics Manual by Crow, Davis, Maxfield):
- The population has a normal distribution.
- The sample is a random sample.
The test statistic under the null distribution is $$chi^2 = dfrac{(n-1)s^2}{sigma^2} = dfrac{(20-1)(20)}{8} = 47.5text{.}$$
I'm not sure what significance level you're using, but from here, it should be pretty straightforward.
answered Feb 9 '15 at 3:43
Clarinetist
10.8k42778
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
Hypotheses:
$H_0: sigma^2 = 8$
$H_1: sigma^2 neq 8$
This is a $chi^2$ test for one variance problem.
Assumptions (taken from Statistics Manual by Crow, Davis, Maxfield):
- The population has a normal distribution.
- The sample is a random sample.
The test statistic under the null distribution is $$chi^2 = dfrac{(n-1)s^2}{sigma^2} = dfrac{(20-1)(20)}{8} = 47.5text{.}$$
I'm not sure what significance level you're using, but from here, it should be pretty straightforward.
answered Feb 9 '15 at 3:43
Clarinetist
10.8k42778
add a comment |
Hypotheses:
$H_0: sigma^2 = 8$
$H_1: sigma^2 neq 8$
This is a $chi^2$ test for one variance problem.
Assumptions (taken from Statistics Manual by Crow, Davis, Maxfield):
- The population has a normal distribution.
- The sample is a random sample.
The test statistic under the null distribution is $$chi^2 = dfrac{(n-1)s^2}{sigma^2} = dfrac{(20-1)(20)}{8} = 47.5text{.}$$
I'm not sure what significance level you're using, but from here, it should be pretty straightforward.
answered Feb 9 '15 at 3:43
Clarinetist
10.8k42778
add a comment |
Hypotheses:
$H_0: sigma^2 = 8$
$H_1: sigma^2 neq 8$
This is a $chi^2$ test for one variance problem.
Assumptions (taken from Statistics Manual by Crow, Davis, Maxfield):
- The population has a normal distribution.
- The sample is a random sample.
The test statistic under the null distribution is $$chi^2 = dfrac{(n-1)s^2}{sigma^2} = dfrac{(20-1)(20)}{8} = 47.5text{.}$$
I'm not sure what significance level you're using, but from here, it should be pretty straightforward.
answered Feb 9 '15 at 3:43
Clarinetist
10.8k42778
Hypotheses:
$H_0: sigma^2 = 8$
$H_1: sigma^2 neq 8$
This is a $chi^2$ test for one variance problem.
Assumptions (taken from Statistics Manual by Crow, Davis, Maxfield):
- The population has a normal distribution.
- The sample is a random sample.
The test statistic under the null distribution is $$chi^2 = dfrac{(n-1)s^2}{sigma^2} = dfrac{(20-1)(20)}{8} = 47.5text{.}$$
I'm not sure what significance level you're using, but from here, it should be pretty straightforward.
answered Feb 9 '15 at 3:43
Clarinetist
10.8k42778
answered Feb 9 '15 at 3:43
Clarinetist
10.8k42778
answered Feb 9 '15 at 3:43
Clarinetist
10.8k42778
answered Feb 9 '15 at 3:43
Clarinetist
10.8k42778
10.8k42778
add a comment |
add a comment |
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