2018 J-TERM MIDTERM Non-Computer Portion
- What is the definition of a pvalue?
The probability of observing a result by random chance that is as extreme or more extreme than what was observed assuming that the null hypothesis is true.
T/F (2pts each) Simply write True or False in the blank at the end of the statement.
- For a left tailed test, if the test statistic is less than the critical value, the correct conclusion is to fail to reject the Ho. __F__
- If you increase alpha, the power will increase. ___T____
- All other things equal, if you increase the confidence, the interval will get wider. ___T____
- For a fixed alpha, will never be bigger than , no matter what the sample size. ___F____
- If the effect size increases (the distance between the null mean and assumed actual mean) the power will decrease. ___F___
- For a two sample confidence interval for the difference in means (µ1-µ2), if both limits are positive, that is evidence that the two population means are not equal and that µ1 is bigger. ___T____
- The adjusted R2 will never be larger than the R2. ___T____
- When adding variables to a regression model, the R2 will never decrease. ___T____
- You get a data set and before you look at the data, you find that the sample linear correlation coefficient r is equal to 0.003. You can safely conclude that the two variables are not associated with one another. ___F*____
- Stepwise selection will eliminate only variables that are not related to the response. ___T*____
- Multicollinearity is present when predictors (not the response) are significantly linearly correlated with one another. ___T___
(Question 13 and 14) Assume the results in the ANOVA table below came from an experiment in which the mean depths of artifacts found at different archeological sites were tested to see if there was any evidence of this mean depths being different.
|
|
|
|
|
|
- (2 pts each) Given the ANOVA table above, find:
- The Mean Square Error: 7346
- The F Value: 42
- R2: = 176.45/238 = .7414
- How many degrees of freedom were used in estimating the MSE? 13
- How many archeological sites were being compared in this study? (How many separate means are there in the separate means model? 4
|
- Given that the 95th percentile of the F3,13 distribution is 3.51 ( ) conduct a 6 step hypothesis test to test the claim that at least one pair of mean depths are different. (You do not need to draw and shade step 2 here, but do identify the critical value.) Also, you may assume the assumptions are met.
- Ho: µ1= µ2 = µ3 =µ4 F = 12.42 6.
Ha: At least 1 pair are different 4. P-value < 0.05
- CV= 3.41 Reject H0
- Consider again the archeological site example from the last question. It is thought that the depth of the artifacts is a good indicator of the age of the site. The deeper the artifact, the older the site is thought to be. This time, assume we were comparing 6 sites to see if there was evidence that one of the sites was the oldest (biggest mean depth). In order to do this we compared all the group means to each other … each pair of mean depths was compared and the results from their analysis in R is below.
- Note that multiple comparison corrections were not made to these tests. How would we correct these pvalues if we were to make a Bonferroni correction?
Multiply the p-values by 6
- Is there any evidence that there is a site that is the oldest (the mean depth is the deepest)? Support your answer with statistics and/or evidence from the output above (ie pvalue(s)).
For sites E and F, when comparing them to the other sites their p-values are statistically significant (p < 0.001). This indicates the mean depth for sites E and F are different from all the other sites’ mean depths. The difference between sites E and F are also statistically significant (p-value = 0.00749). This estimated difference for F – E is -5.7717; indicating the mean depth of site E is larger than that of site F. Therefore, site E has the deepest mean depth and is the oldest site.