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# CONFIDENCE INTERVAL AND HYPOTHESIS TEST

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Author: Christine Farr
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http://theperfecthomework.com/confidence-interval-and-hypothesis-test/

Confidence Interval and Hypothesis Test:Carbon Monoxide (CO) is a colourless and odourless gas. Even at low levels of exposure, carbon monoxide can cause serious health problems. A home is considered safe if the mean CO concentration is 5.0 parts per million (ppm) or lower. We take a random sample of 8 readings in various locations and they are recorded below:5.8, 5.3, 5.7, 5.3, 5, 5.3, 4.9, 4.8The mean and standard deviation for these 8 measurements are 5.262 and 0.358, respectively. Carbon monoxide levels in the home are known to follow a normal distribution.(a) A 90% confidence interval for the true mean CO level in the house is ( ___ , ___ ). (Round values to two decimal places.)(b) We would like to conduct a hypothesis test at the 10% level of significance to determine if the house is unsafe. What is the appropriate test statistic for this hypothesis test? Choose one below:- zOR- t(c) The hypotheses for the appropriate test of significance are, please choose one below:- H0: u = 5.262 vs. Ha: u < 5.262- H0: u = 5.262 vs. Ha: u > 5.262- H0: u = 5.0 vs. Ha: u > 5.0- H0: u = 5.0 vs. Ha: u <5.0(d) The value of the appropriate test statistic (rounded to two decimal places) is _____.(e) The P-value of the test is between ____ and _____ . We record the weekly grocery bill for a random sample of 11 Canadian households. The mean and standard deviation of weekly grocery expenses for these 11 households are \$114.55 and \$27.76, respectively. Weekly grocery expenses are known to follow a normal distribution.(f) A 99% confidence interval for the true mean weekly grocery bill for all Canadian households is ( ____ , ____ ). (Give the values to two decimal places.)We would like to conduct a hypothesis test at the 1% level of significance to determine whether the true mean weekly amount spent on groceries for all Canadian households differs from \$102. (g) The hypotheses for the appropriate test of significance are, please choose one below:- H0: u = 114.55 vs. Ha: u > 114.55- H0: u = 102 vs. Ha: u > 102- H0: u = 114.55 vs. Ha: u cannot equal 114.55- H0: u = 102 vs. Ha: u cannot equal 102- H0: X BAR = 102 vs. Ha: X BAR cannot equal 102- H0: X = 114.55 vs. Ha: X > 114.55- H0: X BAR = 114.55 vs. Ha: X BAR cannot equal 114.55- H0: X BAR = 102 vs. Ha: X BAR > 102

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