Question

A manufacturer has developed a new fishing line, which the company claims has a mean breaking strength of 15 kilograms with a standard deviation of 0.5 kilogram. To test the hypothesis that µ = 15 kilograms against the alternative that µ < 15 kilograms, a random sample of 50 lines will be tested. The critical region is defined to be xbar < 14.9. a) Find the probability of committing a type I error when H_0 is true.

Answer 1

Answer:

0.0786

Step-by-step explanation:

Given :

Mean, u = 15

Standard deviation = 0.5

Sample size = 50

Critical region, x' < 14.9

Acceptance region will be, x' ≥ 14.9

H0 : u = 15

H1 : u < 15

P(type I error)

= P(x' < 14.9 when u = 15)

$P(\frac{x' - u}{\sigma / \sqrt{n}} < \frac{14.9 - 15}{0.5/ \sqrt{50}})$

P(z < -1.414)

From the standard distribution table

NORMSDIST(-1.414) = 0.0786