Testing of hypothesis, Interpreataion of linear correlation

1. When using the F-statistic for hypothesis testing of the variance, which sample variance is the numerator and which sample variance is the denominator?

2. How do you interpret the linear correlation coefficient?

3. How do you test the equality of population variances?

4.How do you test the significant differences between treatment means?

Solution Preview

1 When using the f-statistic for hypothesis testing of the variance, which sample variance is the numerator and which sample variance is the denominator?

Numerator: Variance among the sample means
Denominator: Within sample variance

2. How do you interpret the linear correlation coefficient?

When one variable increases as the other increases the correlation is positive; when one decreases as the other increases it is negative. The complete absence of correlation is represented by 0.

The primary measure of linear correlation is the Pearson product-moment correlation coefficient (which is symbolized by the lower-case Roman letter r). The value of r ranges in value from r=+1.0 for a perfect positive correlation to r= -1.0 for a perfect ...

Solution Summary

The following posting answers four questions on F-statistic for hypothesis testing of the variance, linear correlation, equality of population variances, differences between treatment means.

The following is a sample
Quiz #1 Final
7 34
4 25
2.5 24
8 34
3 20
7.5 34
7.25 42
7 25
5 33
Conduct a hypothesis test to determine if there is a linear relationship (positive correlation) between the two scores or not. Remember to clearly state the null and alternate hypothesis and assume α = .05.

1. Using data consisting of diamond price and carat (weight) for thirty randomly selected diamonds, a correlation between price and weight was found to be 0.767. At the 0.01 level of significance, is there a positive association between the two variables? Show all 5 steps in the hypothesis testing process.
2. Kendra Korbi

1. Results from regressing the spread between Corporate AAA bonds and the Treasury 10-year note on GDP are provided in the attached file.
a) Test the hypothesis:
Ho: Intercept = 0; Ha: Intercept =/= 0
Ho: Slope = 0; Ha: Slope =/= 0
b) Calculate the correlation between the regression residuals t and (t - 1).
c) Test the hyp

1. Describe the "third variable problem" as it relates to correlation and provide an example of how you might see this played out in your own field.
2. How does hypothesis testing contribute to the scientific knowledge base? Now that you have a general understanding of hypothesis testing, provide an example of how you might

6. a. Compute the correlation between age in months and number of words known.
b. Test for the significance of the correlation at the .05 level of significance.
c. Interpret this correlation.
(see attached file for data)

1. When we have a straight-line relation between two variables, we use a Pearson correlation coefficient. What does this coefficient describe?
2. How are deviation scores used in assessing the relation between variables?
3. What are the null and research hypotheses for correlations?
4. Describe the third assumption of

The following hypothesis are given:
Ho: p less or equal to 0
H1: p >0
A random sample of 12 observations indicated a correlation of .32 Can we conclude that the correlation in the population is greater than 0? Use the .05 significance level.
Ho is rejected if t> 1.714
t= .32SQRT 32-5/SQRT 1-(.32)^=?
I don't know

Describe the error in the conclusion:
There is a linearcorrelation between the number of cigarettes smoked and the pulse rate. As the number of cigarettes increases the pulse rate increases. Conclusion: Cigarettes cause the pulse rate to increase.