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Question
Math
Posted 7 months ago

Leandro wants to build a one-sample zz interval with 98%98 \% confidence to estimate the proportion of light bulbs that arrive broken upon shipment to his store. He takes a random sample of 500 bulbs and finds that 25 arrived broken.

What critical value zz^{*} should Leandro use to construct this confidence interval?

Choose 1 answer:
(A) z=1.96z^{*}=1.96
(B) z=2.054z^{*}=2.054
(C) z=2.326z^{*}=2.326
(D) z=2.576z^{*}=2.576
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Answer from Sia
Posted 7 months ago
Solution by Steps
step 1
Identify the confidence level for the z-interval
step 2
The confidence level given is 98%
step 3
Locate the z-score that corresponds to the 98% confidence level
step 4
From the asksia-ll calculation list, the z-score for a 98% confidence interval is found to be between -2.32635 and 2.32635
step 5
Since confidence intervals use the positive z-score, we select z* = 2.326
[1] Answer
C. z* = 2.326
Key Concept
Critical Value for Confidence Interval
Explanation
The critical value (z*) for a confidence interval is the z-score that corresponds to the desired level of confidence. For a 98% confidence interval, the z-score is approximately 2.326.

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