Question

4) Variance in drug weights is critical in the pharmaceutical industry. For a specific drug with weights measured in grams if the variance is greater than 0.28 the drug could be ineffective. A sample of 18 pills provided a sample variance of 0.36.
(a) Is there evidence to say that the drug variance is too high to be effective with 95% confidence?

(b) Construct a 90% confidence interval for the population variance.

Answer 1

(a)

: Variance of a specific drug weight

Null hypothesis : Ho : = 0.28

Alternative Hypothesis : H1 : > 0.28

Right tailed test

Sample size : Number of pills in the sample :n=18

Sample variance : s2 = 0.36

: Hypothesized Variance = 0.28

For right tailed test :

Degrees of freedom =n-1=18=17

For 17 degrees of freedom,

p-value = 0.1903

for 95% confidence = (100-95)/100 =0.05

As p-Value i.e. is greater than Level of significance i.e (P-value:0.1903 > 0.05:Level of significance); Fail to Reject Null Hypothesis.

There is not sufficient evidence to conclude that the drug variance is too high to be effective.

(b)

confidence interval for the population variance.

for 90% confidence level = (100-90)/100 =0.10

/2 = 0.05

1-/2 = 0.95

Degrees of freedom = n-1 =18-1 =17

Fro 17 degrees of freedom ,

90% confidence interval for the population variance

90% confidence interval for the population variance = (0.2218 ,0.7059 )