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Answer:
The p-value of the test is 0.0301 > 0.02, which means that there is not sufficient evidence at the 0.02 level to support the company's claim.
Step-by-step explanation:
The company's promotional literature claimed that under 64% fail in the first 1000 hours of their use.
At the null hypothesis, we test if the proportion is of at least 64%, that is:
At the alternative hypothesis, we test if the proportion is of less than 64%, that is:
The test statistic is:
In which X is the sample mean, is the value tested at the null hypothesis,
is the standard deviation and n is the size of the sample.
64% is tested at the null hypothesis:
This means that
A sample of 900 computer chips revealed that 61% of the chips fail in the first 1000 hours of their use.
This means that
Value of the test statistic:
P-value of the test and decision:
The p-value of the test is the probability of finding a sample proportion below 0.61, which is the p-value of z = -1.88.
Looking at the z-table, z = -1.88 has a p-value of 0.0301.
The p-value of the test is 0.0301 > 0.02, which means that there is not sufficient evidence at the 0.02 level to support the company's claim.