uantitative Methods 1) Briefly describe the difference between null hypothesis and alternative hypothesis. (2) 2) How do you decide whether you can reject or not reject a null hypothesis? Describe two possible ways to assess a hypothesis. (2) 3) What is the difference between a one sample and a two sample test? (2) 4) Which are the two different kinds of mistakes that we can make in a hypothesis test? What are their respective general probabilities? How do, again in general, these two probabilities relate? (3) 5) Employees at a firm produce units at a rate of 125 per hour, with a standard deviation of 25 units per hour. A new employee is tested on 40 separate random occasions, and is found to have an average output of 105 units per hour. Does this indicate that the new employee's output is significantly different (at the 5% level) from the average output in the firm? (2) 6) Based upon collected data, a local car dealer has estimated that the amount spent on extras in cars is normally distributed with an average of $2,200 per customer. She is interested in the question, whether lately, that average may have changed. Data concerning the purchase of extras by the last nine customers shows the following amounts were spent (in $): 2350, 2486, 1935, 1524, 3221, 2489,1790, 1866, and 2247. Test whether the amounts spent on extras have, in fact, changed, or not. (2) 7) Calculate the critical values for a test, for a significance level of 1% and a sample size of 17, for (a) two tail, (b) upper one tail, (c) lower one tail. (1.5) 8) For testing the effectiveness of a drug, 900 subjects receive an oral administration of the drug in question. Another 1000 subjects receive a placebo. What is a suitable null hypothesis in this case? You can evaluate whether the drug has an effect on the test subjects by using a standardized scale. For the group having received the drug in question (n=900), the mean test score was 9.78, with a standard deviation of 4.05. For the control group (n=1000), the mean test score was 15.10, with a standard deviation of 4.28. At the 0.1% significance level, can you reject your null hypothesis? (2.5)