![Statistics: The Art and Science of Learning from Data (4th Edition)](https://www.bartleby.com/isbn_cover_images/9780321997838/9780321997838_largeCoverImage.gif)
Good friends and marital status Is the number of good friends associated with marital status? For GSS data with marital status measured with the categories (married, widowed, divorced, separated, never married), an ANOVA table reports F = 0.80 based on df1 = 4, df2 = 612.
- a. Introduce notation and specify the null hypothesis and the alternative hypothesis for the ANOVA F test.
- b. Based on what you know about the F distribution, would you guess that the test statistic value of 0.80 provides strong evidence against the null hypothesis? Explain.
- c. Software reports a P-value of 0.53. Explain how to interpret it.
a.
![Check Mark](/static/check-mark.png)
State the hypotheses and describe the notations.
Answer to Problem 36CP
Null hypothesis:
Alternative hypothesis:
Explanation of Solution
Given that
State the hypotheses:
Null hypothesis:
That is, all the means are equal.
Alternative hypothesis:
That is, at least one pair of means differ.
Here,
b.
![Check Mark](/static/check-mark.png)
Check whether test statistics value of 0.80 provide strong evidence against the null hypothesis.
Explanation of Solution
If F statistic is 1, then the null hypothesis will be accepted. If the F statistic is more than 1, then null hypothesis will be rejected.
Here, the value of F statistic is 0.8, which is close to 1. Thus, it does not provide strong evidence against the null hypothesis.
c.
![Check Mark](/static/check-mark.png)
Interpret
Explanation of Solution
Rejection rule:
If
Conclusion:
Here, the P-value is 0.53.
Here,
That is, P-value is greater than the 0.05.
Therefore, the null hypothesis is not rejected.
Thus, there is not enough evidence to conclude that at least one pair of population mean is not equal.
Want to see more full solutions like this?
Chapter 14 Solutions
Statistics: The Art and Science of Learning from Data (4th Edition)
- Examine the Variables: Carefully review and note the names of all variables in the dataset. Examples of these variables include: Mileage (mpg) Number of Cylinders (cyl) Displacement (disp) Horsepower (hp) Research: Google to understand these variables. Statistical Analysis: Select mpg variable, and perform the following statistical tests. Once you are done with these tests using mpg variable, repeat the same with hp Mean Median First Quartile (Q1) Second Quartile (Q2) Third Quartile (Q3) Fourth Quartile (Q4) 10th Percentile 70th Percentile Skewness Kurtosis Document Your Results: In RStudio: Before running each statistical test, provide a heading in the format shown at the bottom. “# Mean of mileage – Your name’s command” In Microsoft Word: Once you've completed all tests, take a screenshot of your results in RStudio and paste it into a Microsoft Word document. Make sure that snapshots are very clear. You will need multiple snapshots. Also transfer these results to the…arrow_forward2 (VaR and ES) Suppose X1 are independent. Prove that ~ Unif[-0.5, 0.5] and X2 VaRa (X1X2) < VaRa(X1) + VaRa (X2). ~ Unif[-0.5, 0.5]arrow_forward8 (Correlation and Diversification) Assume we have two stocks, A and B, show that a particular combination of the two stocks produce a risk-free portfolio when the correlation between the return of A and B is -1.arrow_forward
- 9 (Portfolio allocation) Suppose R₁ and R2 are returns of 2 assets and with expected return and variance respectively r₁ and 72 and variance-covariance σ2, 0%½ and σ12. Find −∞ ≤ w ≤ ∞ such that the portfolio wR₁ + (1 - w) R₂ has the smallest risk.arrow_forward7 (Multivariate random variable) Suppose X, €1, €2, €3 are IID N(0, 1) and Y2 Y₁ = 0.2 0.8X + €1, Y₂ = 0.3 +0.7X+ €2, Y3 = 0.2 + 0.9X + €3. = (In models like this, X is called the common factors of Y₁, Y₂, Y3.) Y = (Y1, Y2, Y3). (a) Find E(Y) and cov(Y). (b) What can you observe from cov(Y). Writearrow_forward1 (VaR and ES) Suppose X ~ f(x) with 1+x, if 0> x > −1 f(x) = 1−x if 1 x > 0 Find VaRo.05 (X) and ES0.05 (X).arrow_forward
- Joy is making Christmas gifts. She has 6 1/12 feet of yarn and will need 4 1/4 to complete our project. How much yarn will she have left over compute this solution in two different ways arrow_forwardSolve for X. Explain each step. 2^2x • 2^-4=8arrow_forwardOne hundred people were surveyed, and one question pertained to their educational background. The results of this question and their genders are given in the following table. Female (F) Male (F′) Total College degree (D) 30 20 50 No college degree (D′) 30 20 50 Total 60 40 100 If a person is selected at random from those surveyed, find the probability of each of the following events.1. The person is female or has a college degree. Answer: equation editor Equation Editor 2. The person is male or does not have a college degree. Answer: equation editor Equation Editor 3. The person is female or does not have a college degree.arrow_forward
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
![Text book image](https://www.bartleby.com/isbn_cover_images/9780079039897/9780079039897_smallCoverImage.jpg)