Question

The dosage of a drug in a particular tablet needs to be precise. It is essential that the tablets contain 57.63⁢mg of the active ingredient with a variance of 0.03. A random sample of 25 tablets finds that the variance of the active ingredient is 0.0294. Does the data suggests at α=0.05 that the variance of the drug in the tablets is less than the desired amount? Assume the population is normally distributed.

Steps:  :  

1.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.

2. reject or fail to reject?

3. What is the conclusion?

Answer 1

a)

H0: = 0.03

Ha: < 0.03

Test statisitcs

= ( n - 1) S2 /

= 24 * 0.0294 / 0.03

= 23.52

df = n - 1 = 24

critical value at 0.05 significance level with 24 df = 13.848

b )

Since test statistics > 13.848 , Fail to reject null hypothesis.

c)

We conclude that we do not have sufficient have sufficient evidence to support the claim that

the variance of the drug in the tablets is less than the desired amount.