Question

26. A sample of 1100 computer chips revealed that 62% of the chips fail in the first 1000 hours of their use. The company's promotional literature states that 60% of the chips fail in the first 1000 hours of their use. The quality control manager wants to test the claim that the actual percentage that fail is different from the stated percentage. State the null and alternative hypotheses.

H0:

Ha:

27. A sample of 1100 computer chips revealed that 62% of the chips fail in the first 1000 hours of their use. The company's promotional literature states that 60% of the chips fail in the first 1000 hours of their use. The quality control manager wants to test the claim that the actual percentage that fail is different from the stated percentage. Make the decision to reject or fail to reject the null hypothesis at the 0.10 level.

Answer 1

26) H₀: P = 0.60

     H_a: P = 0.60

27) The test statistic z = (p - P)/sqrt(P(1 - P)/n)

                                    = (0.62 - 0.6)/sqrt(0.6 * 0.4/1100)

                                    = 1.354

At alpha = 0.1, the critical values are z_0.05 = +/- 1.645

As the test statistic value is not greater than the upper critical value (1.354 < 1.645), so we should not reject the null hypothesis.

So there is not sufficient evidence to support the claim that the actual percentage that fail is different from the stated percentage.