Answer:
a. (23.4%, 38.9%)
Step-by-step explanation:
Р = x/∝ = 52/167 = 0.3114
At 95% confidence level
∝ = 1 - 0.95 = 0.05
Zerit = Z0.05/2 = 1.96
Р ± Zerit [tex]\sqrt{P(1-P) / n}[/tex]
= 0.3114 ± 1.96 [tex]\sqrt{0.3114(1-0.3114) / 167}[/tex]
= 0.3114 ± 0.0702
= 0.2412 or 0.3816
= 24.1% or 38.1%
Closest Option = 23.4%, 38.9%
A 95% confidence interval for the true percentage of individuals whose favorite animal is a dog is (23.4%, 38.9%)
The formula for calculating the confidence interval based o proportion is expressed according to the formula:
[tex]p\pm z\sqrt{\frac{p(1-p)}{n} }[/tex]
z is the z-score at 95% confidence interval
p is the proportion
n is the sample size
Given the following parameters
p = 52/167 = 0.31
z = 1.96
n = 167
Substitute the given parameters into the formula to have:
[tex]CI=0.31 \pm 1.96\sqrt{\frac{0.31(1-0.31)}{167} } \\CI=0.31 \pm 1.96\sqrt{\frac{0.31(0.69)}{167} } \\CI=0.31 \pm 1.96(0.035)\\CI=0.31\pm 0.0701\\CI = (0.31-0.0701, 0.31+0.0701)\\CI=(0.234, 0.389)[/tex]
Hence a 95% confidence interval for the true percentage of individuals whose favorite animal is a dog is (23.4%, 38.9%)
Learn more on confidence interval here: https://brainly.com/question/17212516
