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One and Two (or more) Sample Hypothesis Testing Paper. Using data from one of the data sets available through the “Data Sets” link on your page, develop one business research question from which you will formulate a research hypothesis to test one population parameter and another to test two (or more) population parameters. Formulate both a numerical and verbal hypothesis statement regarding each of your research issue. Perform Hypotheses Tests using the five step model. Describe and interpret the results of the test, both in statistical terms and in conversational English.
Include appropriate descriptive statistics. Solution: Research question: To find whether there is a significant difference between wins and salary of the baseball players.
There are two leagues denoted as 1 if American League and 0 if National League We have separated the data set as Data set American League. Hypothesis Test: Independent Groups (t-test, pooled variance) Salary -mil Wins 75.479 81.71 mean 45.930 13.07 std. 14 14 n 26 df -6.2357 difference (Salary -mil - Wins) 1,140.1793 pooled variance 33.7665 pooled std. 12.7626 standard error of difference 0 hypothesized difference -0.49 t.6292 p-value (two-tailed) The test statistic value is -0.49. The p value for the test statistic is 0.6292. Conclusion: Since the p value of test statistic is greater than 0.05 level of significance we may accept the null hypothesis H0 at 5% level of significance.
Hence, we conclude that there is no significant difference between wins and salary- mil of the baseball players in American League. Research question: To find whether there is a significant difference between wins and salary of the baseball players. Data set National League. Regression Analysis R² 0.810 Adjusted R² 0.788 n 30 R 0.900 k 3 Std. Error 4.988 Dep.
Wins ANOVA table Source SS df MS F p-value Regression 2,757.1594 3 919.0531 36.94 1.60E-09 Residual 646.8406 Total 3,404.0000 29 Regression output confidence interval variables coefficients std. Error t (df=26) p-value 95% lower 95% upper Intercept 1.84 0.053.9583 -70.13 Batting 492.4490 140.3025 3.510.0017 204.0532 780.8449 ERA -15.9575 1.6753 -9.525 5.78E-10 -19.4011 -12.5139 HR 0.1035 0.0289 3.582.0014 0.0441 0.1628 The regression equation is Wins = 1.8499 + 492.4490 Batting -15.9575 ERA + 0.1035 HR Here all the p values of the coefficients are less than 0.05 i.e. Are significant at 5% level of significance.
The R2 value is slightly reduced after dropping the variables and it is of not that much effect and hence the model is good. Correlation: Research question: To find whether salary have relationship with Attendance of the baseball players. There are two leagues denoted as 1 if American League and 0 if National League We have separated the data set as Data set American League. Correlation Matrix Salary -mil Attendance Salary -mil 1.000 Attendance.895 1.000 14 sample size The correlation coefficient between salary- mil and attendance is 0.895. There is a strong positive correlation exist between the variables. Null Hypothesis: H0: ρ=0 H0: “no linear relationship” between the variables. Alternative Hypothesis: H1: ρ≠0 H1:“ linear relationship” between the variables.
Level of significance: α = 0.05 Critical value: At 5% level of significance t distribution with v = 14 - 2 degrees of freedom is 2.178813 Test statistic: Under has a t distribution with v = n-2 degrees of freedom. R= 0.895 and n = 14 Conclusion: Since the test statistic value is greater than the critical value there is no evidence to accept the null hypothesis at 5% level of significance. Hence we conclude that there is a relationship exist between the variables salary- mil and attendance. Data set National League.