Question

# In order for a new drug to be sold on the market, the variance of the...

In order for a new drug to be sold on the market, the variance of the active ingredient in each dose should be 0.03mg. A random sample of 25tablets with a dosage strength of 56.57mg is taken. The variance of the active ingredient from this sample is found to be 0.01920.0192. Does the data suggests at α=0.005 that the variance of the drug in the tablets is less than the desired amount? Assume the population is normally distributed.

Step 3 of 5:

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

We have to test the hypothesis that

Variance of active ingredient is less than 0.03

i.e. Null Hypothesis -

against

Alternative Hypothesis - ( Left-tailed test)

We use chi-square test to test significance of population variance.

The value of chi-square test statistic is

Given :

Value of chi-square test statistic = 15.36

Degrees of freedom = n-1 =24

Alpha: level of significance = 0.05

Since test is left-tailed and value of test statistic is 15.36, p-value is obtained by

p-value = 0.0902

Decision: Since p-value > level of significance, we failed to reject the null hypothesis.

Conclusion: There is insufficient evidence to claim that the Variance of active ingredient is less than 0.03.

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