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Zagat Survey Case Study Part III

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Case Study III: Inferential Statistics

This part of the case study will explore the application of inferential statistics to the Zagat Survey sample data. In Part II, claims were made that attempted to extrapolate the sample data to the population, but they were statistically invalid. So here in Part III, I will properly project the sample data into the population and compare it to the previous methods. Earlier in the study, the univariate estimate used was simply the mean value of the sample taken for the variable Cost. But this does not account for the presence of variation in a sample that could affect the mean. We can use this value within a standard normal distribution of sample means to try and narrow down the true …show more content…

Both of these values, along with the test statistic, are provided in the Excel regression output. An online F-value calculator1 produced a Critical F-Value of 2.704. As outlined in Appendix C, we reject the null hypothesis and conclude that the regression is in fact useful. Using the same null and alternative hypotheses, the same test can be performed for the regression between Décor and Cost. In this case, we reject the null hypothesis and confirm the alternative, which states that Décor (being the only independent variable) does in fact affect the Cost. So there is a direct relationship between the Décor and Cost. The multiple regression model does a good bob of predicting the Cost. As seen in Part II of the case study, the regression produced a relatively high Adjusted R Square value of .76406, which means that about 76% of the variation in Cost can be explained by the other variables (Appendix D). We can also see from this output that each variable is given a t-Stat value. All of these values are higher than the Critical T-Value (from T-distribution table) for 99 degrees of freedom all the way up to the significance level of 1% (t = 2.364). And, as shown before, the F-Value hypothesis testing for the regression as a whole proved that the regression was in fact useful. So all of these claims when used in concert provide strong evidence that this model has a high predictive value. The best estimation for Cost is going to be the

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