1. The makers of a new home furnace system claim that if the furnace is installed in Midwestern homes, homeowners will observe an average fuel bill of no more than $80.00 per month during January if their house has between 2,000 and 2,200 square feet of heated living space. Suppose the manufacturer wants to test this claim so they hire an agency to test the claim by taking a random sample of homes of this size where the new furnace has just been installed.
a. If the desired significance level for the test is 0.01, what conclusion should be made about the company's claim if the sample of 64 homes results in a sample means bill of $81.40 and a sample standard deviation of $25? Hint: Use a one-tail test and compare the t-statistic versus the critical value of t.
b. Repeat (a), but this time use the p-value approach for a two-tail test.
c. Suppose a consumer agency wishes to place the burden of proof on the manufacturer. Would a one-tail test or a two-tail test put more burden on the manufacturer? Explain. Be careful as you think about this question.
2. Business ethics is an issue that has increasingly permeated the news. How has this discussion and the cases which have involved less than scrupulous behavior affected company policy? In 2008 the Conference Board proclaimed that 41% of companies had their own ethics code. In a 2013 survey conducted by the Conference Board, 97 of 124 companies indicated they now have their own ethics code.
a. Is there evidence that there has been a change in the proportion of companies with ethics codes? Use the appropriate critical value test methodology to answer this question. Conduct your test at the 0.05 significance level.
b. Is there evidence that there has been an increase in the proportion of companies with ethics codes? Use the appropriate critical value test methodology to answer this question. Conduct your test at the 0.05 significance level.
3. The manager of a local grocery store believes that the store's average daily sales are more than $8,000 per day. To test his belief, a sample of 64 days of sales was selected and it was found that the average sale was $8,250 with a sample standard deviation of $1,200. Test the manager's belief using a significance level of .01. What conclusion should be made about the manager's claim? Next, find the p-value and explain its meaning.