Question

A machine in a factory must be repaired if it produces more than 10% defectives in production. A random sample of 100 items from a day's production contains 15 defectives, and the foreman says that the machine must be repaired. Statistically, does the sample evidence support his decision to repair at the 0.01 significance level? Conduct a test by using both the critical region method and the p-value method.

Answer 1

Answer:

No

Step-by-step explanation:

Sample size, n = 100 ; number of defective, x = 15

Phat = x / n = 15 / 100 = 0.15

H0 : P = 0.1

H0 : P > 0.1

The test statistic :

(Phat - P) / [P(1 - P) / n]

(0.15 - 0.1) / √[0.1(1 - 0.1) / 100]

0.05 / 0.03

Test statistic = 1.667

α = 0.01

The Pvalue ;

df = n - 1 ; 100 - 1 = 99

Pvalue(1.667, 99) = 0.049

Pvalue > α ; WE fail to reject the Null

Critical value = 2.364

Test statistic < critical value ; we fail to reject the Null

Hence, result is is not significant