3 questions - statistics related Assignment Example | Topics and Well Written Essays - 500 words

3 questions - statistics related - Assignment Example According to the table above, the mean average miles per gallon are 28.3792 when the total sample of purchasers is 24. In the same manner, out of the 24 sampled data, the sample variance is 8.859 whereas the sample standard deviation is 2.97643 as shown in the SPSS output table above. Under the sample of 24, which is below 30, the most appropriate statistical test, using the 0.5 significance level is the student’s t-distribution test. Under this test, the sample must be 30 or less, and the arithmetic mean is not normally distributed. According to the output table above, the Adjusted R squared is 0.030, meaning that only 3% of the variables explain the dependent variable Int. 2. The adjusted R squared helps in predicting how the regression model predicts responses for the explained observations. In this case, it is the fraction by which the variance of the errors that depends on the sum of squares is less than the variance of the dependent variables. Thus, as argued above, only 3% of the independent variables can predict the dependent variable statistically. When the ANOVA test is run in determining the means among populations, the f statistical value versus the critical value are determined. Under the corrected model, the f statistics is 3.227. Under the assumptions of the hypothesis tests, when the f statistic in attest is lower than the critical f value, then the null hypothesis is rejected. The value obtained means that under the purchase intensions implied by the data above, the null hypothesis is accepted and the independent variables in the states sampled explain the purchase variations. Also as shown in the second table, the means of the states in terms of consumptions are 37.0.18, 50.357, and 51.459 for the states IL, LA, and TX respectively. The standard error is also 4.339, 4.965, and 4.597 respectively as shown in the table