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) $z^{*}=2.576$

Question

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) $z^{*}=2.576$

Accepted Answer

∻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.⚹◊What formula can be used to calculate the critical value z* in a one-sample z-interval for estimating a proportion?⍭ Generate me a similar question◊

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