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Stranded Bank wants to determine whether or not there is asignificant difference between the branch (X15) used and theattitudinal items (X7 – X12). What stat...

Question

Stranded Bank wants to determine whether or not there is asignificant difference between the branch (X15) used and theattitudinal items (X7 – X12). What statistical test should berun?Select one:a. Frequency tabulationsb. Cross tabulation and Chi-squarec. One sample t-testsd. Independent sample t-testse. Levene’s testf. Paired sample t-testg. One-way ANOVAh. Correlationi. Regressionj. Factor analysis

Stranded Bank wants to determine whether or not there is a significant difference between the branch (X15) used and the attitudinal items (X7 – X12). What statistical test should be run? Select one: a. Frequency tabulations b. Cross tabulation and Chi-square c. One sample t-tests d. Independent sample t-tests e. Levene’s test f. Paired sample t-test g. One-way ANOVA h. Correlation i. Regression j. Factor analysis



Answers

A stock analyst wondered whether the mean rate of return of financial, energy, and utility stocks differed over the past 5 years. He obtained a simple random sample of eight companies from each of the three sectors and obtained the 5-year rates of return shown in the following table (in percent): $$\begin{array}{|c|c|c|} \hline \text { Financial } & \text { Energy } & \text { Utilities } \\ \hline 10.76 & 12.72 & 11.88 \\ \hline 15.05 & 13.91 & 5.86 \\ \hline 17.01 & 6.43 & 13.46 \\ \hline 5.07 & 11.19 & 9.90 \\ \hline 19.50 & 18.79 & 3.95 \\ \hline 8.16 & 20.73 & 3.44 \\ \hline 10.38 & 9.60 & 7.11 \\ \hline 6.75 & 17.40 & 15.70 \\ \hline \end{array}$$ (a) State the null and alternative hypotheses. (b) Verify that the requirements to use the one-way ANOVA procedure are satisfied. Normal probability plots indicate that the sample data come from normal populations. (c) Are the mean rates of return different at the $\alpha=0.05$ level of significance? (d) Draw boxplots of the three sectors to support the results obtained in part (c).

Here we have a set of data and using what we know about linear regression, coefficient of correlation and hypothesis testing, we're going to determine whether or not we can conclude from the set that there is a significant linear correlation. If we were to input this data into our graphing calculator and graph the scatter plot of it, we would get something that looks similar to this, which in essence, is fairly linear. So it seems as though using the coefficient of correlation will indeed be a good measure of correlation so long as it's significant, considering that the coefficient of correlation is best used in linear functions going ahead and also in your graphing calculator running the linear Regression T test, we'll find that we have in our value So our coefficient of correlation, which is equal to 0.816 That's a relatively strong and positive correlation here. But in order to determine whether or not that significant, we also need to look at our P value That was out that our calculators gave us. So here it has given us a P value equal to 0.2 If we were testing this at a significance level of 0.5 we could indeed include that. This is significant. So our coefficient coefficient of correlation equal 2.816 is indeed a good measure of the correlation here. And if we had completed this without first using a scatter plot, we may have tried to use our r squared value, which may not have been accurate or if we had instead seen that are scatter. Plot was not linear. If it had, you know, a curve to it, a non linear graph, then we would have erroneously concluded that the coefficient of correlation was a good measure. But in this case, we actually did not miss anything. So that is good news, and we can conclude that there is a strong and positive correlation between X and y here.


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