ECON 3406: Non-Excel Problem Set #1 1. Find the mean and standard deviation of the following sample of numbers: 1, 5, 5, 9, 2, 3, 6, 10, 4. 2. Suppose that the average amount of money per month at Chick-fil-A is $47.35 with standard deviation of $12.22; further assume the sample is normally distributed. (a) What is the probability of spending less than $40 at Chick-fil-A per month? (b) What is the probability of spending between $30 and $60 at Chick-fil-A per month? (c) What is the probability of spending above $75 per month? (d) Consider a time x such that less than 80 percent of monthly spends are less than x. What is x? (e) Suppose you take a sample of 25 individuals. What is the probability that their sample average is less than $40? 3. A sample of 41 observations from a lab is processed. The sample weight of those observations is 5.4 milliliters, with standard deviation of 2.33 milliliters. (a) Construct 90, 95 and 99 percent confidence intervals by using z-scores. (b) Construct 90, 95 and 99 percent confidence intervals, but replace the critical values with the t table critical values. 4. The upstairs HVAC of a house breaks. The homeowner believes it should around $7,000 to replace the whole system. She contacts 12 local contractors and receives a sample average estimate of $7,945 with standard deviation of $1,540. (a) Write down an appropriate null and alternative hypothesis. (b) Construct a test statistic. (c) Write down the appropriate critical values. (d) Test your hypothesis at all appropriate levels. 5. Upon graduation from UWG, you consider upgrading your current vehicle. You are looking for a mid-level sedan (Altima, Accord, e.g.) and want to estimate your car payment. You believe the car payment will be more than $400 per month. One night, you try 20 different combinations of sedans that you want based on your trade-in and get a sample average of $429, with standard deviation of $67. (a) Write down an appropriate null and alternative hypothesis. (b) Construct a test statistic. (c) Write down the appropriate critical values. (d) Test your hypothesis at all appropriate levels. 6. The Food Network has a number of cooking shows where a restaurant chef challenges a celebrity, such as Bobby Flay. The chefs believe that their customers will increase after being on the show. 22 episodes are sampled; the average number of customers before is 78 per evening, while the average amount after is 83.8. The standard deviation of the prices is 15.72. (a) Write down an appropriate null and alternative hypothesis. (b) Construct a test statistic. (c) Write down the appropriate critical values. (d) Test your hypothesis at all appropriate levels. 1