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Answer:
Yes, we have sufficient evidence at the 0.02 level to support the company's claim.
Step-by-step explanation:
We are given that a sample of 1500 computer chips revealed that 32% of the chips do not fail in the first 1000 hours of their use. The company's promotional literature claimed that above 29% do not fail in the first 1000 hours of their use.
Let Null Hypothesis, : p
0.29 {means that less than or equal to 29% do not fail in the first 1000 hours of their use}
Alternate Hypothesis, : p > 0.29 {means that more than 29% do not fail in the first 1000 hours of their use}
The test statics that will be used here is One-sample proportions test;
T.S. = ~ N(0,1)
where, = proportion of chips that do not fail in the first 1000 hours of their use = 32%
n = sample of chips = 1500
So, <u>test statistics</u> =
= 2.491
<em>Now, at 0.02 level of significance the z table gives critical value of 2.054. Since our test statistics is more than the critical value of z so we have sufficient evidence to reject null hypothesis as it fall in the rejection region.</em>
Therefore, we conclude that more than 29% do not fail in the first 1000 hours of their use which means we have sufficient evidence at the 0.02 level to support the company's claim.