A correlation coefficient for Bee Taylor's Department Store in Mayberry, NC, between sales ability and amount of sales is Sales ability is measured on an interval scale and amount of sales is measured on a ratio scale. Note that the correlation was conducted on 42 sales employees. Test this coefficient by using a t test and Table B.2. This test was mentioned in "Tech Talk" on page 263. However, the author never showed the formula, which can be found in many statistics books.

Below is the "famous" formula.

t = r . This formula tells you to multiply the coefficient by the square root of the df divided by the difference of 1 and the coefficient squared. Note that n = sample size; df (degrees of freedom) = the sample size decreased by 2.

H0: and H1:

(a) Critical value t at 5% risk =

(b) Obtained test statistic (Show procedure.): t =

(c) Decision on H0:

(d) What conclusion do you reach about sales ability and amount of sales? Are these variables at Bee's correlated?

Review the problem above.

(a) What percent of sales volume is explained by sales ability?

(b) Express the relationship between sales ability and sales volume that is suggested by the correlation coefficient. Write in terms of strength and direction of the relationship.

a) Critical value t at 5% risk = ± 2.02
b) Obtained test statistic (Show procedure.): t = 6.376
c) on H0: Reject the H0. ...

Solution Summary

The solution provides step by step method for the calculation of t test statistic for correlation coefficients . Formula for the calculation and Interpretations of the results are also included.

For the accompanying data set (a) draw a scatter diagram (b) compute the correlationcoefficient rounded to three decimal places and (c) determine rather there is a linear relation between x and y
Data Set
x 2 6 6 7 9
y 8 7 6 9 5

A correlationcoefficient computed for n=18 and a=0.10 is r=0.692. . Using the t -testfor the correlationcoefficient, what are the critical values?
A) +1.734 B) +2.120 C) +1.746 D) +2.101

Given that two variables have a correlationcoefficient of 0.70, use the formula for the t testfor the CorrelationCoefficient to determine if the correlationcoefficient is significant. Assume a sample size of 17 and alpha =0.05. Show all steps.

QUESTIONS:
(a) How does correlation analysis differ from regression analysis?
(b) What does a correlationcoefficient reveal?
(c) State the quick rule for a significant correlation and explain its limitations.
(d) What sums are needed to calculate a correlationcoefficient?
(e) What are the two ways of testing a correlati

Given the following information, use Table B.4, which is; values of the correlationcoefficient needed for rejection of the null hypothesis. I'm certain you have access to said table. Use the table to determine whether the correlations are significant and how you would interpret the results.
The correlation between speed and

(a) Make a scatter plot of the data. What does it suggest about the correlation between X and Y? (b) Use Megastat or Excel to calculate the correlationcoefficient. (c) Use Excel to find t.05 for a two-tailed test. (d) Calculate the t test statistic (e) Calculate critical value of ra. (f) Can you reject p=0?
Orders(X)

(1) Draw a scatter plot and a quantile-quantile plot based on these two variables.
(2) Normalize the two variables based on z-score normalization.
(3) Calculate the correlationcoefficient. Are these two variables positively or negatively correlated?

Coastal State University is conducting a study regarding the possible relationship between the cumulative grade point average and the annual income of its recent graduates. A random sample of 151 Coastal State graduates from the last five years was selected, and it was found that the sample correlationcoefficient between cumul

X 38 61 38 49 44
Y 57 42 44 55 28
a) construct scatter diagram
b) compute linear correlationcoefficient
c) comment on relationship
-positive linear association
-negative linear association
-little to no evidence of a linear association.

The coefficient of correlation was computed to be -0.60. This means
a. the coefficient of determination is .
b. as X increase Y decreases.
c. X and Y are both 0.
d. as X decreases Y decreases.
Which of the following is a stronger