Discrete Components Inc.manufactures a line of electrical resistors.Presently, the carbon composition line is producing 100 ohm resistors.The population variance of these resistors "must not exceed 4" to conform to industry standards.Periodically, the quality control inspectors check for conformity by randomly select 10 resistors from the line, and calculating the sample variance.The last sample had a variance of 4.36.Assume that the population is normally distributed.Using $\alpha$ = 0.05, the appropriate decision is ___.
A)increase the sample size
B)reduce the sample size
C)reject the null hypothesis
D)do not reject the null hypothesis
E)maintain status quo

Question

Quizplus · Accepted Answer

In this case, we need to test whether the sample variance of 4.36 is significantly greater than the population variance of 4. We can use an F-test to compare these variances. 
The null hypothesis is that the population variance is equal to 4, and the alternative hypothesis is that the population variance is greater than 4. 
Using a significance level of 0.05 and 9 degrees of freedom (10-1), we can find the critical F-value to be 3.18. 
The calculated F-value is 4.36/4 = 1.09. Since this calculated F-value is less than the critical F-value, we cannot reject the null hypothesis. 
Therefore, we conclude that there is not enough evidence to suggest that the population variance exceeds 4, and we should maintain the status quo.

Discrete Components Inc α\alphaα = 005, the Appropriate Decision Is ___

Discrete Components Inc $\alpha$ = 005, the Appropriate Decision Is ___