Question

A drug which is used for treating cancer has potentially dangerous side effects if it is taken at an improper dosage. The drug is manufactured at two different plants, plant A and plant B. A medical researcher believes that tablet A has a smaller variance in dosage than the variance in dosage from tablet B. The sample variance of a sample of 13 dosages of tablet A is 0.01. The sample variance of a sample of 18 dosages of tablet B is 0.016. Test the claim using a 0.1 level of significance. Let σ21 represent the population variance for tablet A.

Step 1 of 5 : State the null and alternative hypotheses for the test.

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. (Reject the null hypothesis or fail to reject the null hypothesis)

Step 5 of 5: What is the conclusion? (Is there sufficient evidence or not)

Answer 1

The drug is manufactured by two different plants A & B. We have to test that tablet A has a smaller variance in dosage than the variance in dosage from tablet B.

Hence, hypothesis is stated as -

H0 :   i.e. tablet A has variance in dosages as same as that of variance of tablet B in dosages.

H1 :   i.e. tablet A has a smaller variance in dosage than the variance in dosage from tablet B.

Given that sample variance of a sample of 13 dosages of tablet A is 0.01 & sample variance of a sample of 18 dosages of tablet B is 0.016.

We have to test the claim using a = 0.1 level of significance.

H0 can be tested by the F-test.

Test statistic -

F =

[ Note : s12  is taken to be larger variance ]

Given :

s12 = 0.016, n1 = 18, s22 = 0.01, n2 = 13

Test criterion :

H1 is one sided i.e. , reject H0 if F F,{(n1 - 1),(n2 - 1)}

[Note : The value of statistic F never negetive]

Calculations :

Test statistic -

F =

=

F =

observed value of F -

F,{(n1 - 1),(n2 - 1)} = F0.1,{(18 - 1),(13 - 1)} = F0.1,(17,12) = 2.0839 = 2.084

Hence, F F,{(n1 - 1),(n2 - 1)} we reject H0 at 0.1 level of significance.

Conclusion :

There is sufficient evidence that tablet A has a smaller variance in dosage than the variance in dosage from tablet B.