Question

The National Institutes of Health agreed to supply active disease viruses, such as polio and AIDS, to research firms for the purpose of experimentation. A process is set up to automatically fill millions of small test tubes to an average of 9.00 ml of disease virus with standard deviation .35 ml. (a) Given a sample size of 49 test tubes, establish a Type I error risk of 2% and find the ĉ cutoffs for accepting u = 9.00 ml ū= Cutoff for accepting u = 9.00ml is from to ī = (b) Using the cutoff in part (a), calculate the probability of a Type II error for a shift to u = 8.85 ml. Write your answer as a decimal with four decimal places. B= (

Answer 1

(a)

Standard error of sample mean =
a/Vn
= 0.35 /
V49
= 0.05

z value for 2% Type I error = 2.326 (For 2%, the cutoff significance level is 2%/2 = 0.01 and 1 - 2%/2 = 0.99)

Margin of error = z * Std error = 2.326 * 0.05 = 0.1163

Cutoff for accepting $\mu$ = 9.00 ml is

(9 - 0.1163, 9 + 0.1163)

from $\bar{x}$ = 8.8837 to $\bar{x}$ = 9.1163

(b)

Probability of Type II error = P(Accepting hypothesis | $\mu$ = 8.85) = P(8.8837 < $\bar{x}$ < 9.1163 | $\mu$ = 8.85)

= P[(8.8837 - 8.85)/0.05 < z < (9.1163 - 8.85)/0.05]

= P[0.674 < z < 5.326]

= P[z < 5.326] - P[z < 0.674]

= 1 - 0.7498

= 0.2502