# A drug, which is used for trea

A drug, which is used for treating cancer, has potentiallydangerous side effects if it is taken in doses which are largerthan 41.54mg , the required dosage for the treatment. It isimportant that the variance of the amount of the active ingredientis 0.04. 12 tablets are randomly selected and the amount of thedrug in each tablet is measured. It is determined that the varianceof the amount of active ingredient is 0.0291mg . Does the datasuggests at α=0.01 that the variance of the drug in the tablets isless than the desired amount? Assume the population is normallydistributed.

Step 1 of 5:

State the null and alternative hypotheses. Round to four decimalplaces when necessary.

Step 2 of 5:

Determine the critical value(s) of the test statistic. If thetest is two-tailed, separate the values with a comma. Round youranswer to three decimal places.

Step 3 of 5:

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

Step 4 of 5:

Make the decision to reject the null hypothesis or fail toreject the null hypothesis.

Step 5 of 5:

What is the conclusion? Is there sufficient evidence or is therenot sufficient evidence?

Here, we perform Chi-square test for One population variance as:

Hence, there is not sufficient evidence to conclude that thevariance of the drug in the tablets is less than the desired amountat 1% level of significance.

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