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 0.022. 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.

1b. 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.

1c. Determine the value of the test statistic. Round your answer to three decimal places.

1d. Make the decision. ( Reject Null Hypothesis/  Fail to Reject Null Hypothesis)

1e. 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

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: σ^2 = 0.022
Alternative Hypothesis, Ha: σ^2 < 0.022

1b)

Rejection Region
This is left tailed test, for α = 0.025 and df = 17
Critical value of Χ^2 is 7.564
Hence reject H0 if Χ^2 < 7.564

1c)

Test statistic,
Χ^2 = (n-1)*s^2/σ^2^2
Χ^2 = (18 - 1)*0.0118/0.022
Χ^2 = 9.118

1d)

Fail to Reject Null Hypothesis

1e)
There is not sufficient evidence to show that the amount of active ingredient has a variance that is less than the desired amount.