A study claims that all homeowners in a town spend an average of 8 hours or more on house cleaning and gardening during a weekend. A researcher wanted to check if this claim is true. A random sample of 20 homeowners taken by this researcher showed that they spend an average of 7.68 hours on such chores during a weekend. The population of such times for all homeowners in this town is normally distributed with the population standard deviation of 2.1 hours.
a. Using a 1% significance level, can you conclude that the claim that all homeowners spend an average of 8 hours or more on such chores during a weekend is false? Use both approaches.
b. Make the test of part a using a 2.5% significance level. Is your decision different from the one in part a? Comment on the results of parts a and b.