Business

RES342 March 12, 2012 Introduction Hypothesis testing is used to determine the correct answer and obtain a conclusion. This is usually done through gaining research, testing research and drawing conclusions from that research. Hypothesis testing includes selecting a hypothesis, creating a null hypothesis, creating an alternative hypothesis, finding the t-value and comparison of the results in order to choose the best possible solution. This paper will discuss Team B’s steps in finding a null hypothesis as well as an alternative hypothesis. These will be created based upon data obtained from baseball statistics. Specifically we will analyze the correlation between aattendance and number of wins that a team has. The five-step hypothesis test will be used to decide whether to or not to reject the null hypothesis. Hypothesis A hypothesis is a statement based on a guess about the relationship between two variables. Hypothesis testing is used in making decisions every day by researchers, managers and other business people. When determining a hypothesis the first step is to come up with an idea, and develop a statement that we will prove or disprove our idea. The hypothesis statement must include a null hypothesis and an alternate hypothesis. One statement must be true, the other false, opposing each other. Our hypothesis is based on attendance in baseball stadiums that may be directly related to the number of wins a team has. The steps in hypothesis testing are as follows: idea, formulate the hypothesis, design the experiment, set up a decision rule, collect data, make a decision and possibly revise ideas if the hypothesis did not turn out the way you had planned (Doane & Seward, 2007). Statement Attendance in the baseball stadiums are tied directly to the number of wins that a team has. Attendance reaches 2 million or more only if a team has 69 or more wins, otherwise the attendance is below 2 million. H0: µ ≥ 69 H1: µ < 69 Null: Attendance in the baseball stadiums will reach 2 million or greater only if a team has 69 or more wins. H0: µ ≥ 69 Alternate: Attendance in the baseball stadiums will reach 2 million even if the number of team wins is below 69. H1: µ < 69 This is a Left-Tailed Test This is a one-sample test, analyzing the number of wins in an equation, the attendance is being used as an indicator. Level of Significance The level of significance, tells us what the chances are of accepting or rejecting the null hypothesis. This tells us if our statement is true or false. The level of significance is also known as the probability of making a Type I error. According to Doane and Seward when choosing a smaller α, like 0.01, it is harder to reject the null hypothesis (Doane & Seward, 2007). In our example we are using a 99% significance, or α = .01. α = P(reject H0/ H0 is true) 0.10 = P(reject H0/ H0 is true) Determine the Test Statistic Determining which test statistic is based on the sample size and a normal distribution. The z statistic is used for a normal distribution or a sample > than 30. The t statistic is used for samples with less than 30 observations or if the sample has a large standard deviation. We will use the z statistic our sample is of a normal distribution with 30 observations (Doane & Seward, 2007). The z test statistic in our sample is as follows: Test Statistic: Z Since we have a small sample size (n = 30 ≥ 30), therefore we used the z test-statistic: [pic] [pic] [pic] [pic] Decision Rule The decision rule is used to determine the criteria of accepting or rejecting our null hypothesis. This step includes determining the critical value, either for the z value or the t value, depending on the sample size, and the sample error. Our sample is 30 determining that we will use the z test value. The z value will show the variance of the sample estimate from the expected value (Doane & Seward, 2007). The critical value is the value that divides the sample distribution into two regions, the reject region, and the accept region. The reject region is when we will reject the null hypothesis. The accept region is when we will accept the null hypothesis as true. There are three types of decision rules, they are two- tailed test, left tailed, and right tailed tests. The two tailed test rule states to reject the null hypothesis if the test statistic is less than the left tailed critical value or if the test statistic is greater than the right tailed critical value. The left tailed test rules states you reject the null hypothesis if the test statistic is less than the left tailed critical value. The right tailed test rules states you reject the null hypothesis if the test statistic is greater than the right tailed critical value (Doane & Seward, 2007). An alternate method that can be used is to determine the p-value, which is used when the sample test statistic is larger then the value from our data. If the p value is smaller then the level of significance then we reject the null hypothesis. If it larger we accept the null hypothesis (Doane & Seward, 2007). The p value of our data set is 0.086 Decision Rule: Type 1 error P = 0.086 α = .01 α/2=.01/2=.005 z .005 = ± 0.086 Analyzing Data Analyzing the data and drawing a conclusion is the next step. This step includes the statistical data of determining is the null hypothesis true or false. For a Left-tailed Test, reject H0 if z < 0.086 or if z > -0.086. Conclusion The objective of this assignment was for Team B to provide a hypothesis, create a null and alternative hypothesis and based upon the data to create a conclusion and select whether to accept the null hypothesis. The baseball statistics were used to obtain the wins and attendance for each baseball team. Team B then used those statistics to find if there was a correlation in attendance in the baseball stadiums are tied directly to the number of wins that a team has. We believe that attendance reaches 2 million or more only if a team has 69 or more wins, otherwise the attendance is below 2 million. We were able to accept the null hypothesis which is: if attendance in the baseball stadiums will reach 2 million or greater only if a team has 69 or more wins. Reference Doane, D. P., & Seward, L. E. (2007). Applied Statistics in Business and Economics. New York, NY: McGraw-Hill/Irwin.