Question

A grinding machine will be qualified for a particular task if it can be shown to produce less than 8% defective parts. In a random sample of 300 parts, 14 were defective. On the basis of these data, can the machine be qualified? Find the P-value and state a conclusion.

- The P-value is .0170 Round the answer to four decimal places [incorrect]

- We can conclude that the machine can be qualified.[correct]

my work..

np0 = 24

n(1-np0)= 276

p = 14 / 300 = .0467 (because problem states to round to four decimal places)

Op = sqrt( .08 (1-.08 )) / 300 = .0157

.0467 - .08 / .0157 = -2.12

Z = .0170, but this is wrong. WHY AM I GETTING THIS PROBLEM wrong? what am i doing wrong?

I've used .05 - .08 / .0157 also, and this gives me the wrong answer also.

Answer 1

Solution :

This is the left tailed test .

The null and alternative hypothesis is

H₀ : p = 0.08

H_a : p < 0.08

= x / n = 14 / 300 = 0.0467

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.0467 - 0.08 / [(0.08 * 0.92) / 300]

z = -2.128

P-value = 0.0167

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