Question

Chapter 9 Froum

Answer each question, Interpret your interval in words. You will be able to see what others have posted after you post your response. You can post only once. I will grade the first post only. You may use your T84

Q1) The New York Times and CBS News conducted a nationwide poll of 1050 randomly selected 13- 17-year-olds. We can consider the sample to be a simple random sample. Of these 1050 teenagers, 690 had a television in their room. Construct a 95% confidence interval for the proportion of all people in this age group who had a TV in their room at the time of the poll

Q2) Apartment rental rates. You want to rent an unfurnished one-bedroom apartment for next semester. The mean monthly rent for a random sample of 10 apartments advertised in the local newspaper is $540 with a standard deviation of $87. Construct a 95% confidence interval for the mean monthly rent for unfurnished one-bedroom apartments available for rent in this community.

Answer 1

1)

sample proportion, = 0.6571
sample size, n = 1050
Standard error, SE = sqrt(pcap * (1 - pcap)/n)
SE = sqrt(0.6571 * (1 - 0.6571)/1050) = 0.0146

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, Zc = Z(α/2) = 1.96

Margin of Error, ME = zc * SE
ME = 1.96 * 0.0146
ME = 0.0286

CI = (pcap - z*SE, pcap + z*SE)
CI = (0.6571 - 1.96 * 0.0146 , 0.6571 + 1.96 * 0.0146)
CI = (0.6285 , 0.6857)

h
we are 95% confident that the proportion of all people in this age group who had a TV in their room at the time of the poll is between 0.6285 and 0.6857

2)

sample mean, xbar = 540
sample standard deviation, s = 87
sample size, n = 10
degrees of freedom, df = n - 1 = 9

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, tc = t(α/2, df) = 2.262

ME = tc * s/sqrt(n)
ME = 2.262 * 87/sqrt(10)
ME = 62.232

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (540 - 2.262 * 87/sqrt(10) , 540 + 2.262 * 87/sqrt(10))
CI = (477.77 , 602.23)

we are 95% confident that the mean monthly rent for unfurnished one-bedroom apartments available for rent in this community is between (477.77 , 602.23)