Deck 21: Chi-Square Tests for the Variance or Standard Deviation

Question 1

TABLE 12-20
A filling machine at a local soft drinks company is calibrated to fill the cans at a mean amount of 12 fluid ounces and a standard deviation of 0.5 ounces.The company wants to test whether the standard deviation of the amount filled by the machine is 0.5 ounces.A random sample of 15 cans filled by the machine reveals a standard deviation of 0.67 ounces.
True or False: Referring to Table 12-20,the decision is to reject the null hypothesis when using a 10% level of significance.

Answer 1

True

Question 2

TABLE 12-20
A filling machine at a local soft drinks company is calibrated to fill the cans at a mean amount of 12 fluid ounces and a standard deviation of 0.5 ounces.The company wants to test whether the standard deviation of the amount filled by the machine is 0.5 ounces.A random sample of 15 cans filled by the machine reveals a standard deviation of 0.67 ounces.
True or False: Referring to Table 12-20,there is sufficient evidence to conclude that the standard deviation of the amount filled by the machine is not exactly 0.5 ounces when using a 10% level of significance.

Answer 2

True

Question 3

TABLE 12-20
A filling machine at a local soft drinks company is calibrated to fill the cans at a mean amount of 12 fluid ounces and a standard deviation of 0.5 ounces.The company wants to test whether the standard deviation of the amount filled by the machine is 0.5 ounces.A random sample of 15 cans filled by the machine reveals a standard deviation of 0.67 ounces.
Referring to Table 12-20,the parameter of interest in the test is ________.

Answer 3

population standard deviation or population variance

Question 4

TABLE 12-20
A filling machine at a local soft drinks company is calibrated to fill the cans at a mean amount of 12 fluid ounces and a standard deviation of 0.5 ounces.The company wants to test whether the standard deviation of the amount filled by the machine is 0.5 ounces.A random sample of 15 cans filled by the machine reveals a standard deviation of 0.67 ounces.
Referring to Table 12-20,what type of test should be performed?

A)Lower-tail test
B)Upper-tail test
C)Two-tail test
D)None of the above.

Question 5

TABLE 12-20
A filling machine at a local soft drinks company is calibrated to fill the cans at a mean amount of 12 fluid ounces and a standard deviation of 0.5 ounces.The company wants to test whether the standard deviation of the amount filled by the machine is 0.5 ounces.A random sample of 15 cans filled by the machine reveals a standard deviation of 0.67 ounces.
True or False: Referring to Table 12-20,the p-value of the test is somewhere between 5% and 10%.

Question 6

TABLE 12-20
A filling machine at a local soft drinks company is calibrated to fill the cans at a mean amount of 12 fluid ounces and a standard deviation of 0.5 ounces.The company wants to test whether the standard deviation of the amount filled by the machine is 0.5 ounces.A random sample of 15 cans filled by the machine reveals a standard deviation of 0.67 ounces.
Referring to Table 12-20,what are the lower and upper critical values of the test when allowing for 5% probability of committing a type I error?

Question 7

TABLE 12-20
A filling machine at a local soft drinks company is calibrated to fill the cans at a mean amount of 12 fluid ounces and a standard deviation of 0.5 ounces.The company wants to test whether the standard deviation of the amount filled by the machine is 0.5 ounces.A random sample of 15 cans filled by the machine reveals a standard deviation of 0.67 ounces.
True or False: Referring to Table 12-20,in order to perform the test,you need to assume that the amount filled by the machine follows a normal distribution.

Question 8

TABLE 12-20
A filling machine at a local soft drinks company is calibrated to fill the cans at a mean amount of 12 fluid ounces and a standard deviation of 0.5 ounces.The company wants to test whether the standard deviation of the amount filled by the machine is 0.5 ounces.A random sample of 15 cans filled by the machine reveals a standard deviation of 0.67 ounces.
True or False: Referring to Table 12-20,the decision is to reject the null hypothesis when using a 5% level of significance.

Question 9

TABLE 12-20
A filling machine at a local soft drinks company is calibrated to fill the cans at a mean amount of 12 fluid ounces and a standard deviation of 0.5 ounces.The company wants to test whether the standard deviation of the amount filled by the machine is 0.5 ounces.A random sample of 15 cans filled by the machine reveals a standard deviation of 0.67 ounces.
True or False: Referring to Table 12-20,there is sufficient evidence to conclude that the standard deviation of the amount filled by the machine is not exactly 0.5 ounces when using a 5% level of significance.

Question 10

TABLE 12-20
A filling machine at a local soft drinks company is calibrated to fill the cans at a mean amount of 12 fluid ounces and a standard deviation of 0.5 ounces.The company wants to test whether the standard deviation of the amount filled by the machine is 0.5 ounces.A random sample of 15 cans filled by the machine reveals a standard deviation of 0.67 ounces.
Referring to Table 12-20,what is the value of the test statistic?

Question 11

TABLE 12-20
A filling machine at a local soft drinks company is calibrated to fill the cans at a mean amount of 12 fluid ounces and a standard deviation of 0.5 ounces.The company wants to test whether the standard deviation of the amount filled by the machine is 0.5 ounces.A random sample of 15 cans filled by the machine reveals a standard deviation of 0.67 ounces.
Referring to Table 12-20,which is the appropriate test to use?

A)χ² test of independence
B)McNemar test
C)Wilcoxon rank sum test
D)χ² test of population variance