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Answer:
The proportion of chips that do not fail in the first 1000 hours of their use is 52%.
Step-by-step explanation:
The claim made by the company is that 52% of the chips do not fail in the first 1000 hours of their use.
A quality control manager wants to test the claim.
A one-proportion <em>z</em>-test can be used to determine whether the proportion of chips do not fail in the first 1000 hours of their use is 52% or not.
The hypothesis can be defined as:
<em>H₀</em>: The proportion of chips do not fail in the first 1000 hours of their use is 52%, i.e. <em>p</em> = 0.52.
<em>Hₐ</em>: The proportion of chips do not fail in the first 1000 hours of their use is different from 52%, i.e. <em>p</em> ≠ 0.52.
The information provided is:
The test statistic value is:
The test statistic value is -1.80.
Decision rule:
If the <em>p-</em>value of the test is less than the significance level then the null hypothesis will be rejected and vice-versa.
Compute the <em>p</em>-value as follows:
*Use a <em>z</em>-table.
The <em>p</em>-value = 0.07186 > <em>α</em> = 0.02.
The null hypothesis was failed to be rejected at 2% level of significance.
<u>Conclusion</u>:
The proportion of chips that do not fail in the first 1000 hours of their use is 52%.