- 1 The Sales Manager For A Hardware Wholesaler Finds That 229 Of The Previous 500 Calls To Hardware Store Owners Resulte 1 (291.28 KiB) Viewed 58 times
1. The sales manager for a hardware wholesaler finds that 229 of the previous 500 calls to hardware store owners resulted in new product placements. Assume that the 500 calls represent a random sample. Find a 95% confidence interval for the long-run proportion of new product placements. Give an interpretation of the 95% confidence interval for the long-run proportion of new product placements. [2 marks] 2. A producer of a product claims that the product will increase output per machine by at least 29 units per hour. A manager installs the product on 15 of the machines, and finds that the average increase was only 26 with a standard deviation of 6.2. What are the null and alternative hypotheses? What is your decision rule specified in terms of critical values of a t-random variable? Use 5% significance level. What is the value of the test-statistic? [2 marks] 3. Jeffrey, as an eight-year old, established a mean time of 16.43 seconds for swimming the 25 yard freestyle. His dad, Frank, thought that Jeffrey could swim the 25-yard freestyle faster using goggles. Frank bought Jeffrey a new pair of expensive goggles and timed Jeffrey for 15 25-yard freestyle swims. For the 15 swims, Jeffrey's mean time was 16 seconds, with a standard deviation of 0.8 seconds. Frank thought that the goggles helped Jeffrey to swim faster than the 16.43 seconds. Conduct a hypothesis test using a = 0.05. [2 marks] 4. Suppose a consumer group suspects that the proportion of households that have three or more cell phones is 30%. A cell phone company has reason to believe that the proportion is not 30%. Before they start a big advertising campaign, they conduct a hypothesis test. Their marketing people survey 150 households with the result that 43 of the households have three or more cell phones. Conduct a hypothesis test using a/2 = 0.05. [2 marks] 5. Suppose that you want to test Ho: µ = 277 against H₁ : μ‡277 at a = 0.10, and you know that the population standard deviation o = 13.5. If you randomly select a sample of 20 observations, for what values of the sample mean will you reject the null hypothesis? [2 marks]