Question

In order for a new drug to be sold on the market, the variance of the active ingredient in each dose should be 0.02mg. A random sample of 25 tablets with a dosage strength of 48.42⁢mg is taken. The variance of the active ingredient from this sample is found to be 0.0048. Does the data suggests at α=0.01 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 4: Compute the value of the test statistic. Round your answer to two decimal places.

Step 3 of 4: Determine the decision rule for rejecting the null hypothesis H0. Round the numerical portion of your answer to three decimal places.

Step 4 of 4: Make the decision for the hypothesis test. Reject or Fail to Reject Null Hypothesis

Answer 1

step 1

To Test :-

H0 :-  

H1 :-  

Step 2

Test Statistic :-

χ² = ( ( 25-1 ) * 0.0048 ) / 0.02
χ² = 5.76

Step 3
Test Criteria :-
Reject null hypothesis if
= 10.856

Step 4
= 5.76 < 10.856 , hence we reject the null hypothesis
Conclusion :- We Reject null hypothesis.