Entire Assignment Must Be Typed For The Computation

Entire Assignment Must Be Typed For The Computation

Your entire assignment must be typed. For the computational problems in Part IV, you only need to show your plugged-in formula for the requested statistic. You do not need to show any computational steps. As always, round your final computational answers to two decimal places. When computing the value of a statistic that leads to your final answer, such as a mean, standard deviation, or standard error, round that answer to two decimal places too, even if it is just used as a step to your final answer. Do not, however, round any of the numbers that you pull from the tables in the back of the book (i.e., critical values). Please don’t hesitate to ask me for help if you get stuck!

Part I: Probability (4 points) Answer the following questions based on what you’ve learned about probability.

1. Four airplanes from different airlines have crashed in the past two weeks. This terrifies Bubbles, who must travel on a plane. Her travel agent claims that the probability of a plane crash is minuscule. Who is correctly interpreting the situation? Why?

2. In a population, μ = 100 and σ_X = 525. A sample (N = 150) has X̄ = 102. Using two tails of the sampling distribution and the .05 criterion: (a) What is the critical value? (b) Is this sample in the region of rejection? How do you know? (c) What does this indicate about the likelihood of this sample occurring in this population? (d) What should we conclude about the sample?

Part II: Statistical Tests (12 points) You recently learned about a number of statistical tests, which are listed below. Indicate which test you would perform in each of the cases that follow, and, then, explain why that would be the appropriate test.

3. You performed a study investigating the effects of time pressure on performance on a verbal task. You had participants complete an anagrams task, where they had to unscramble some scrambled words. Half of the participants were told that they would have to rush in order to get the anagrams completed, and the other half were told that they should have plenty of time to solve them all. The dependent measure was the number of anagrams solved. What type of test would you perform to examine whether the independent variable had a significant effect on anagram performance? How did you determine that this is the test to use?

4. You want to examine how the salary of your employees compares to the average salary in the general population of the U.S. You use Census data to locate the mean and the standard deviation of U.S. salaries and then compute the average salary of all of your 100 employees. What type of test would you perform to see whether your employees have a significantly different salary than that of the general population? How did you determine that this is the test to use?

5. You are researching a new energy drink so you decide to gather 50 participants and assess their energy level both before and after they consume the new energy drink. You ask them to report their energy level on a 1-10 scale just before consuming the drink and then 30 minutes after consuming it. What type of test would you perform to see whether the drink had a significant effect on perceptions of energy level? How did you determine that this is the test to use?

6. You are interested in examining how the GPA of first-generation college students compares to the GPA in the entire university. You gather a sample of 200 first-generation college students and ask them to report their GPA. You are able to access the mean GPA at the university, but no other population parameters are available. What type of test would you perform to see whether these students’ GPA differs significantly from the GPA of the general student population? How did you determine this?

7. You compare the racing speed between professional bicyclists and professional in-line skaters by gathering marathon race times from 30 per group (30 bicyclists & 30 skaters). What type of test would you perform to see whether these students’ GPA differs significantly from the GPA of the general student population? How did you determine this?

8. You want to examine the effects of a speed reading class on reading proficiency. You have an experimental group that attends the class and a control group of participants who do not attend the class. Because you are worried about initial reading ability affecting your reading proficiency dependent measure, you do not split your participants into two groups randomly. Instead, you determine their initial verbal skills based on previously computed standardized test scores. From there, you create pairs of participants with equal verbal skills and assign one participant from each pair to be in the experimental group and the other participant from each pair to be in the control group. What type of test would you perform to see whether the speed-reading class had a significant effect on reading proficiency? How did you determine this?

Part III: Significance Testing (14 points) Answer the following questions.

9. z -Test critical values: If you were performing a two-tailed z -test using an alpha of .05, what positive and/or negative values of z would lead to a statistically significant result? (Be sure to include all values that would be significant.) If you performed a one-tailed z -test using an alpha of .05 and got a z of 1.60, would your result be statistically significant?

10. Imagine you do a two-tailed one-sample t -test with an alpha of .05 on a sample of data from 20 participants and compute a t of -2.19. What critical value of t would you use to determine if your result is significant? Would your result be statistically significant?

11. Imagine that you do a one-tailed one-sample t -test with an alpha of .01 on a sample of data from 28 participants and compute a t of 2.46. What critical value of t would you use to determine if your result is significant? Would your result be statistically significant?

12. Imagine that you computed a correlation between age and salary on a sample of 23 participants and derived a correlation of -.39. Would your result be statistically significant using a two-tailed test with an alpha of .05? Would your result be statistically significant using a one-tailed test with an alpha of .05?

13. Imagine that you do a study comparing job satisfaction of Microsoft employees (which averaged 7.89 on a scale from 1-10) with job satisfaction among Apple employees (which averaged 8.41 on a scale from 1-10). You performed the appropriate statistical test and yielded a nonsignificant result. What would be the most appropriate way of describing the results of the study (be specific in mentioning the relevant variables)? You performed the appropriate statistical test and yielded a statistically significant result. What would be the most appropriate way of describing the results of the study (be specific in mentioning the relevant variables)?

14. Imagine that you do a study correlating the number of years working as a police officer with scores on narcissism and get a correlation of .31. Your result yielded a nonsignificant finding. What would be the most appropriate way of describing the results of the study (be specific in mentioning the relevant variables)? Your result yielded a significant finding. What would be the most appropriate way of describing the results of the study (be specific in mentioning the relevant variables)?

15. Imagine that you do a study and, as a fluke, get a statistically significant result. You rejoice without realizing that you only got your result because of sampling error that occurred by chance. What is the name of this type of error? What is the probability of making this type of error?

Part IV: Computations (10 points) Answer the following computational problems, showing only your plugged-in formulas.

16. If you had a sample size of 10, a sample mean of 44.26, and a standard deviation of 12.31 (this is a standard deviation, not a standard error), between what two means would you find the 95% confidence interval? Show your plugged-in formulas.

17. Compute the z-statistic you would use if you wanted to examine whether the mean age of marriage within a local cult is significantly different from the mean age of marriage in the general population. The data from your cult sample are presented below. You also know that the mean age of marriage in the general population is 29.23, with a population standard deviation of 4.13. Compute z and show your plugged-in formula of z. Your sample: 13, 15, 16, 18, 51, 12, 65. Now compute the appropriate t-test on the data from the previous problem, with the assumption that you only have population information regarding the mean of 29.23 and will have to estimate the standard deviation of the population because it is unknown. Use the computational formula for estimated population standard deviation when computing the standard deviation. Show your plugged-in formula of t.

19. Compute the related samples t on the following data set. Show your plugged-in t-formula. Condition 1 Condition. Compute the independent samples t on the following data set. Assume a standard deviation of 3.30 for Condition 1 and 2.63 for Condition 2. Show your final plugged-in t-formula. Condition 1 Condition.