Question

A sample of 1600 computer chips revealed that 78% of the chips do not fail in the first 1000 hours of their use. The company's promotional literature states that 77% of the chips do not fail in the first 1000hours of their use. The quality control manager wants to test the claim that the actual percentage that do not fail is more than the stated percentage. Is there enough evidence at the 0.02 level to support the manager's claim? .

a) Find the value of the test statistic. Round your answer to two decimal places.

b) Specify if the test is one-tailed or two-tail

c) Determine P- value. Round your answer to four decimal places.

d) Make the decision to reject or fail to reject the null hypothesis.

Answer 1

Let p denotes the true proportion of chips that do not fail in the first 1000hours of their use.

To test against

This is a one-tailed test.

Here

sample proportion

and sample size

The test statistic can be written as

which under H₀ follows a standard normal distribution.

We reject H₀ at 2% level of significance if P-value < 0.02

Now,

The value of the test statistic

P-value

Since P-value = 0.17093 > 0.05, so we fail to reject H₀ at 2% level of significance and we can conclude that the actual percentage that do not fail is not significantly more than 77%.