Respuesta :
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, [tex]H_0[/tex] : p [tex]\leq[/tex] 0.29 {means that less than or equal to 29% do not fail in the first 1000 hours of their use}
Alternate Hypothesis, [tex]H_1[/tex] : 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. = [tex]\frac{\hat p -p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = proportion of chips that do not fail in the first 1000 hours of their use = 32%
n = sample of chips = 1500
So, test statistics = [tex]\frac{0.32-0.29}{\sqrt{\frac{0.32(1-0.32)}{1500} } }[/tex]
= 2.491
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.
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.
