Business statistics analytics
Question 1 A group of investors wants to develop a chain of fast-food restaurants. In determining potential costs for each facility, they must consider, among other expenses, the average monthly electric bill. They decide to sample some fast-food restaurants currently operating to estimate the monthly cost of electricity. They want to be 99% confident of their results and want the error of the interval estimate to be no more than $100. They estimate that such bills range from $600 to $2,500. How large of a sample should they take?
Question 2 Suppose a study reports that the average price for a gallon of self-serve regular unleaded gasoline is $3.16. You believe that the figure is higher in your area of the country. You decide to test this claim for your part of the United States by randomly calling gasoline stations. Your random survey of 25 stations produces the following prices (all in $). Assume gasoline prices for a region are normally distributed. Did the data you obtained provide enough evidence to reject the claim? Use a 1% level of significance. Make sure you clearly state both the null and the alternative hypotheses in full sentences. Following your calculations, clearly state the conclusion in the same manner (do not simply say â€œaccept/reject nullâ€) and explain how you arrived at this conclusion (based on which metrics).
3.27 3.29 3.16 3.2 3.37
3.3 3.33 3.19 3.3 3.34
3.16 3.27 3.27 3.09 3.35
3.15 3.23 3.14 3.05 3.35
3.21 3.14 3.14 3.07 3.1
Question 3 Where do CFOs get their money news? According to Robert Half International, 47% get their money news from newspapers, 15% get it from communication/colleagues, 12% get it from television, 11% from the internet, 9% from magazines, 5% from radio, and 1% do not know. Suppose a researcher wants to test these results. She randomly samples 67 CFOs and finds that 40 of them get their money news from newspapers. Does the test show enough evidence to reject the findings of Robert Half International? Use a = .05. Make sure you clearly state both the null and the alternative hypotheses in full sentences. Following your calculations, clearly state the conclusion in the same manner (do not simply say â€œaccept/reject nullâ€) and explain how you arrived at this conclusion (based on which metrics).
Question 4 To answer this question, use the Data Analysis Toolpack in Excel and select â€œt-Test: TwoSample Assuming Equal Variancesâ€ from the list of available tools. Conduct a hypothesis test using this tool. Explain your answer (how you decided if men spend more or not) and include the output table.
Some studies have shown that in the United States, men spend more than women buying gifts and cards on Valentineâ€™s Day. Suppose a researcher wants to test this hypothesis by randomly sampling 9 men and 10 women with comparable demographic characteristics from various large cities across the United States to be in a study. Each study participant is asked to keep a log beginning 1 month before Valentineâ€™s Day and record all purchases made for Valentineâ€™s Day during that 1-month period. The resulting data are shown below. Use these data and a 1% level of significance to test to determine if, on average, men actually do spend significantly more than women on Valentineâ€™s Day. Assume that such spending is normally distributed in the population and that the population variances are equal.
Make sure you clearly state both the null and the alternative hypotheses in full sentences. Include the output table; then clearly state the conclusion in the same manner (do not simply say â€œaccept/reject nullâ€), and explain how you arrived at this conclusion (based on which metrics).