Significance of correlation coefficient - test statistic

A pharmaceutical company conducts a study to evaluate the relationship between length of time taking drug X and size of tumor. They enlist 2400 patients with the same type of benign tumor who have been on drug X for varying lengths of time (measured in days). They find that the longer the patient is on the drug, the smaller the patient's tumor size (measured in volume). In fact, they report the results as r(2398) = -.21, with significance of p < .0001. What is your initial perception of this information?

What are other ways, beyond looking at the p-value alone, you could use to try to interpret what this outcome of r(2398) = -.21 tells us about the relationship between length of time taking drug X and the size of the tumor? Support your responses.

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Interpretation of Data
A pharmaceutical company conducts a study to evaluate the relationship between length of time taking drug X and size of tumor. They enlist 2400 patients with the same type of benign tumor who have been on drug X for varying lengths of time (measured in days). They find that the longer the patient is on the drug, the smaller the patient's tumor size (measured in volume). In fact, they report the results as r(2398) = -.21, with significance of p < .0001. What is your initial perception of this information?
Answer
Since the p-value is significant, we can conclude ...

Solution Summary

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

You are testing the null hypothesis that there is no linear relationship between two variables, X and Y. From your sample of n=10, you determine that r=0.80.
a. What is the value of tstat?
b. At the a=0.05 level of significance, what are the critical values?
c. Based on your answers to a and b what statistical decision

See attached data file.
Use the attached CIA Economic and Demographic data report on 46 countries. Take the variables literacy rate, population, and GDP for each country, and compute the correlation among variables. In other words, find the correlation between literacy and pupulation, literacy and GDP, and population and GDP.

a) Given the equation: (See attached), what is the calculated t-statistic and is it significant at the 5 percent level? (Hint: Apply 2 rules)
b) Calculate the coefficient of correlation from the information in (a). Write the H_o and H_a. Then, make a decision about the significance of the coefficient of correlation.
c) Wha

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

An assumption for a significancetest of the correlationcoefficient is that the populations, the variance of each variable is the same at each point of the other variable. Are there other assumptions to correlationcoefficient? What happens if these assumptions are not met? What two numbers do you need to figure the t score f

In order for applicants to work for the state department, they must take a test in the language of the country where they plan to work. The data below shows the relationship between the number of years that applicants have studied a particular language and the grades they received on the proficiency exam.
Applicant # 1 2 3 4

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

13.7
You are given the following data for variables x aqnd y
X Y
20 16
18 12
24 18
20 17
22 21
14 10
18 10
______________________________________
a. Plot these variables in scatter-plot format. Based on this plot, what type of relationship appears to exist between the two variab

(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 teststatistic (e) Calculate critical value of ra. (f) Can you reject p=0?
Orders(X)