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aubford9442

03.07.2022

Mathematics

98% Confidence interval: (0.5483,0.6891)

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 257

Number of adults total body length was 28 feet or longer, x = 159

$\hat{p} = \dfrac{x}{n} = \dfrac{159}{257} = 0.6187$

98% Confidence interval:

$\hat{p}\pm z_{stat}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$

$z_{critical}\text{ at}~\alpha_{0.02} = 2.326$

Putting the values, we get:

$0.6187\pm 2.326(\sqrt{\dfrac{0.6187(1-0.6187)}{257}})\\\\ = 0.6187\pm 0.0704\\\\=(0.5483,0.6891)$

is the required 98% confidence interval.

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