Question

Math

Posted 3 months ago

```
Leandro wants to build a one-sample $z$ interval with $98 \%$ 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 $z^{*}$ should Leandro use to construct this confidence interval?
Choose 1 answer:
(A) $z^{*}=1.96$
(B) $z^{*}=2.054$
(C) $z^{*}=2.326$
(D) $z^{*}=2.576$
```

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Answer from Sia

Posted 3 months ago

Solution by Steps

step 2

Locate the z-score that corresponds to the 98% confidence level. According to the asksia-ll calculation list, the z-score for a 98% confidence interval is found between the left and right critical values of -2.32635 and 2.32635

step 3

Since confidence intervals are always positive, we take the positive value of the z-score

[question number] Answer

C

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. It is used to determine the margin of error for the interval.

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