Confidence Interval 1 In 2012 the Humane Society reported th

Confidence Interval 1. In 2012, the Humane Society reported that 30.4% of all U.S. households own at least one cat. Assume these results came from a survey conducted among 10,000 U.S. households, what is the 80% confidence interval that estimates the population proportion of U.S. households that own at least one cat? (Show all work). 2. The same report listed the annual veterinary cost per household (of those owning at least one cat) as being $191. Find an 85% confidence interval for the actual annual mean veterinary cost among U.S. households with at least one cat. (Use the information in part one of this assignment.) please do part #2

Solution

Q1.
Confidence Interval For Proportion
CI = p ± Z a/2 Sqrt(p*(1-p)/n)))
x = Mean
n = Sample Size
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
Sample Size(n)=10000
Sample proportion = x/n =0.304
Confidence Interval = [ 0.304 ±Z a/2 ( Sqrt ( 0.304*0.696) /10000)]
= [ 0.304 - 1.282* Sqrt(0) , 0.304 + 1.28* Sqrt(0) ]
= [ 0.298,0.31]