Question

A machining process produces screws for which the population proportion of screws with defective threads is .10 (10%). A new laser-enhanced process has become available and the developer claims that the population proportion of screws with defective threads will be less than .10. To test the validity of this claim, 900 screws produced by the new process are selected at random and the sample proportion of defectives is computed. This result will be used to make a decision as to whether or not the manufacturer should invest in the new process.

7) Which of the following should be used as the alternative hypothesis?

A) p = .10 B) p ? .10 C) p ? .10 D) p > .10 E) p < .10

8) Determine the p-value of the test statistic if p ^ = .076. (Round your answer to 4 decimal places.)

A) .9836 B) .0082 C) -.0082 D) .0164 E) .9918

Answer 1

Solution :

This is the left tailed test .

The null and alternative hypothesis is

H₀ : p = 0.10

H_a : p < 0.10

E) p < .10 alternative hypothesis

= 0.076

P₀ = 0.10

1 - P₀ = 1-0.10 = 0.90

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

=0.076-0.10 / [0.10*(0.90) /900 ]

= -2.40

P(z < -2.4) = 0.0082

P-value = 0.0082

The p-value IS = 0.0082

OPTION B IS CORRECT ANSWER