An instructor wishes to see if the variance

Jaylan Chung

Jaylan Chung

Answered question

2022-03-16

An instructor wishes to see if the variance in scores of her 23 students in one class is less than the variance of the population, which is 225. The variance of the class is 198. Is there enough evidence to support the claim that the variation of the students is less than the population variance at alpha = 0.05?
A. The test is a ... test.
a. left
b. two tail
c. right
B. Determine the critical value.
C. Determine the test statistic, reporting to 2 decimal places.
D. Determine the p value, reporting to 4 decimal places.
E. Based on above, what is the decision?
a. Fail to reject the null hypothesis
b. Reject the null hypothesis

Answer & Explanation

teertallectutl

teertallectutl

Beginner2022-03-17Added 2 answers

Here, the chi-square test is used to compare the sample variance with the population variance.
The hypotheses for the test are given below:
Null hypothesis:
H0:σ2=225.
Alternative hypothesis:
H1:σ2<225.
A. This is a a). left tailed test.
B. The critical value of chi-square distribution at 22 degrees of freedom can be obtained using the excel formula, “=CHISQ.INV(0.05,22)”.
C. Here, the sample variance, s2 is 198.
Population variance, σ2 is 225.
Sample size, n is 23.
The test statistic for Chi-square test is calculated as given below.
χ2=(n1)s2σ2=(231)(198)225=19.36
Computation of P-value:
The two tailed P-value for the chi-square test at 22 degrees of freedom can be obtained using the excel formula, “=CHISQ.DIST(19.36,22,TRUE)”.
Decision rule:
If p-valueα, then reject the null hypothesis. Otherwise, do not reject the null hypothesis.
Conclusion:
Here, p-value (0.377) is greater than the level of significance (0.05).
Therefore, fail to reject the null hypothesis.
There is enough evidence to support the claim that the variance of the students is less than the population variance.

Do you have a similar question?

Recalculate according to your conditions!

New Questions in College Statistics

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?