Question

a sample of 1600 computer chips revealed that 42% of the chips do not fail in the first 1000 hours of their use. the company's promotional literature claimed that above 39% do not fail in the first 1000 hours of their use. is there sufficient evidence at the 0.10 level to support the company's claim? state the null and alternative hypotheses for the above scenario.

Answer 1

Reject this null hypothesis because the p-value (0.0523) is lower than the significance level (0.10) in this case.

Explain the term Null hypothesis?

• The null hypothesis is a common statistical theory that contends that there is no statistical relationship or significance between any two sets of observed data or measured phenomena for any given single observed variable.

Let p represent the fraction of the population.

Taking into account the provided data, we have

Null hypothesis: H0 : p ≤ 0.35.

Alternative hypothesis: H1 : p > 0.35, the test is a right-tailed test since the alternative is right-tailed;

For the stated question-

n = 1000; p' = 0.42.

Test statistics for this sample proportion:

z = (p' - p) / √p(1 - p)/n

Put the values-

z = (0.42' - 0.39) / √0.39(1 - 0.39)/1000

z = 1.94

P-value for this right tailed test is;

P(z > 1.94) = 0.0523

Therefore reject this null hypothesis because the p-value (0.0523) is lower than the significance level (0.10) in this case.

We draw the conclusion that we have enough data to back up the company's claim at the 0.10 level.

To know more about the Null hypothesis, here

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