Question

A study finds that 167 out of 298 seals sampled from an ecosystem are earless. Which of the following gives a 90% confidence interval for the proportion of seals that are earless?Group of answer choices[0.52, 0.60][0.51, 0.61][0.50, 0.62][0.49, 0.63]We don't need a confidence interval, because the proportion of earless seals is clearly just 167/298.

Answer 1

Answer: [0.51,0.61]

Step-by-step explanation: Confidence interval (CI) for proportion is given by:

$p_{hat}$ ± $z.\sqrt{\frac{p_{hat}(1-p_{hat})}{n} }$

$p_{hat}$ is the proportion of seals who are earless.

$p_{hat}$ = $\frac{167}{298}$ = 0.56

z is z-score for 90% CI: z = 1.645

Calculating:

$\frac{167}{298}$ ± $1.645.\sqrt{\frac{0.56(0.44)}{298} }$

0.56 ± $1.645.\sqrt{\frac{0.2464}{298} }$

0.56 ± $1.645*0.029$

0.56 ± 0.048

Lower limit: 0.56 - 0.048 = 0.51

Upper limit: 0.56 + 0.048 = 0.61

A 90% CI for proportion $p_{hat}$ = $0.56$ is [0.51,0.61]