Question

The dosage of a drug in a particular tablet needs to be precise. It is essential that the tablets contain 59.21mg of the active ingredient with a variance of 0.02. A random sample of 18 tablets finds that the variance of the active ingredient is 0.0118. Does the data suggests at α=0.025 that the variance of the drug in the tablets is less than the desired amount? Assume the population is normally distributed

. Step 1 of 5 : State the null and alternative hypotheses. Round to four decimal places when necessary.

Step 2 of 5: Determine the critical value(s) of the test statistic. If the test is two-tailed, separate the values with a comma. Round your answer to three decimal places.

Step 3 of 5: Determine the value of the test statistic. Round your answer to three decimal places.

Step 4 of 5: Make the decision. A: Reject Null Hypothesis B: Fail to Reject Null Hypothesis

Step 5 of 5: What is the conclusion? There is sufficient evidence to show that the amount of active ingredient has a variance that is less than the desired amount. There is not sufficient evidence to show that the amount of active ingredient has a variance that is less than the desired amount.

Answer 1

1)

Ho:       σ2	>=	0.02
Ha:        σ2	<	0.02

2)

for 2.5 % level and given df critical values of X2 =

7.564

3)

test statistic X2 =(n-1)s2/ σ2=(18-1)*(0.0118/0.02) =

10.030

4)

since test statistic does not falls in rejection region we fail to reject null hypothesis

5)

There is not sufficient evidence to show that the amount of active ingredient has a variance that is less than the desired amount.