1.) Location is known to affect the number, of a particular item, sold by an automobile dealer. Two different locations, A and B, are selected on an experimental basis. Location A was observed for 9 days and location B was observed for 13 days. The number of the particular items sold per day was recorded for each location. On average, location A sold 39 of these items with a sample standard deviation of 9 and location B sold 51 of these items with a sample standard deviation of 6. Select a 95% confidence interval for the difference in the true means of items sold at location A and B.
2.) An ammunition producer claims his best product has an average lifespan of exactly 14 years. A skeptical customer asks for evidence (data) that might be used to evaluate this claim. The customer was provided data collected from a random sample of 45 people who used the product. Using the data, an average product lifespan of 21 years and a standard deviation of 2 years was calculated. Select the 95%, confidence interval for the true mean lifespan of this product.
3.) An important problem in industry is shipment damage. A windshield factory ships its product by truck and determines that it can meet its profit expectations if, on average, the number of damaged items per truckload is fewer than 12. A random sample of 12 departing truckloads is selected at the delivery point and the average number of damaged items per truckload is calculated to be 11.3 with a calculated sample of variance of 0.49. Select a 95% confidence interval for the true mean of damaged items.