Question

In a random sample of 257 adult Orcas in the wild, there were 159 whose total body length was 28 feet or longer. Create a 98% confidence interval for the population proportion of adult Orcas in the wild who total body length is 28 feet or longer. Enter the lower and upper bounds for the interval in the following boxes, respectively.

Answer 1

Answer:

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.