final eam solutions_ Statistic MBA

final eam solutions_ Statistic MBA - BUS 513 Statistics for...

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BUS 513 – Statistics for Business SSU / Spring 2010 – Newport Beach Campus Nurdan Ozturk May 14, 2010 FINAL EXAM SOLUTIONS #1. Related to Chapter 5: Hypothesis Testing The main goal of statistical inference is to draw a conclusion about the characteristic of a population from sample data. As a result, one of the uses of hypothesis testing is that it involves testing a claim (some prior or well-known fact) about a characteristic of a population, such as the population average, with the use of a sample. In other words, with hypothesis testing we can find out whether or not a sample statistic is “statistically” different from a population parameter. a) Using your own words, explain the meaning of the null hypothesis in hypothesis testing. Null hypothesis is the statement we want to reject. We usually try to falsify the statement using some test on the data. b) Using your own words, explain the meaning of the alternative hypothesis in hypothesis testing. Alternative hypothesis is the statement we want to accept. We usually try to establish the statement using some test on the data. #2. (Related to Hypothesis Testing) Give an example of a hypothesis test in a business setting. Explain in detail. Suppose a store wants to find out if the mean sales have increased after improving the customer care service. He can record the monthly sales before and after the customer service improvement and compare the mean of the both data set. Null hypothesis being the sales are same before and after the improvement of customer service and alternative hypothesis being that the mean sales are different. #3. Related to Chapter 5: Hypothesis Testing When the population standard deviation is known, we compute a Z test statistic for the population average as follows: n X Z σ μ = 1 X
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.where is the sample mean, is the population mean, and n is the sample size. Solution (a) Using your own words, explain the meaning of the non-rejection region in hypothesis testing. In hypotheses testing, the area under distribution curve has divided into two regions, namely rejection region and non-rejection region. Suppose, if the test is of two-tailed, then the critical values (lower and upper critical values) would divide the possible values of the test statistic into two regions called Rejection region and Non-rejection region. The region (or area) below the lower critical value and the region above the upper critical value is called the rejection region, while the region between the two critical values is called the non-rejection region . If the value of the test statistic falls in the rejection region, then the null hypothesis will be rejected. (b) What does it mean when the test statistic Z equals 0 for a 95% confidence level with Z critical values of ± 1.96?
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