A particular professor has noticed that the number of people, P, who complain about his attitude is dependent on the number of cups of coffee, n, he drinks. From eight days of tracking he compiled the following data:

Unless otherwise stated, you can round values to two decimal places.

a) Using regression to find a linear equation for P(n)

P(n) =

b) Find the correlation coefficient

r =

c) Does the correlation coefficient indicate a strong linear trend, a weak linear trend, or no linear trend?

• strong linear trend
• weak linear trend
• no linear trend

d) Interpret the meaning of the slope of your formula in the context of the problem



e) Interpret the meaning of the P intercept in the context of the problem



f) Use your model to predict the number of people that will complain about his attitude if he drinks 10 cups of coffee.



g) Is the answer to part f reasonable? Why or why not?



h) How many cups of coffee should he drink so that no one will complain about his attitude? It is ok to round to one decimal place.

A population of values has a normal distribution with μ = 127.5 and σ = 96.9 . You intend to draw a random sample of size n = 150 .

Find the probability that a single randomly selected value is greater than 114.8. P(x > 114.8) =

Find the probability that a sample of size n = 150 is randomly selected with a mean greater than 114.8. P( ¯ x > 114.8) =

Enter your answers as numbers accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

A researcher would like to know whether there is a significant relationship between Verbal skills and Math skills in population of high school students. A sample of n = 200 students is randomly selected and each student is given a standardized Verbal skills test and a standardized Math skills test.

Based on the test results, students are classified as High or Low in Verbal skills and Math skills.

The results are summarized in the following frequency distribution table (i.e., the numbers represent the frequency count of students in each category):

Based on these results, can the researcher conclude that there is a significant

relationship between Verbal skills and Math skills? Test at the .05 level of significance.

For full credit, your answer must include:

         - hypotheses

         - computed Chi² test for Independence (show all computational steps)

         - computed phi-coefficient to measure the strength of the relationship

         - df and the critical Chi²value for p < .05

         - decision about H₀ and conclusion in the APA reporting format

A recent study claimed that at least 15% of junior high students are overweight. In a sample of 160 students, 18 were found to be overweight. At α = 0.05, test the claim. Identify the claim, state the null and alternative hypotheses, find the critical value, find the standardized test statistic, make a decision on the null hypothesis (you may use a P-Value instead of the standardized test statistic), write an interpretation statement on the decision.

You are conducting a multinomial Goodness of Fit hypothesis test for the claim that the 4 categories occur with the following frequencies:

HoHo : pA=0.1pA=0.1;  pB=0.4pB=0.4;  pC=0.3pC=0.3;  pD=0.2pD=0.2

Complete the table. Report all answers accurate to three decimal places.

What is the chi-square test-statistic for this data?
χ2=χ2=

What is the P-Value?
P-Value =  


For significance level alpha 0.005,

What would be the conclusion of this hypothesis test?

• Reject the Null Hypothesis
• Fail to reject the Null Hypothesis

Report all answers accurate to three decimal places.

Why does the correlation coefficient of a predictor increase when we remove a relevant predictor in a multilinear regression? For example, if we are regressing income on education, gpa, and college rank and then remove college rank from the regression we would see an increase on the correlation coefficient of education and gpa. What is the intuitive explanation for this?

Similarly, we see a decrease in the correlation coefficients when we add a variable. What is the reason for this relationship as well?

9. Researchers record the age and life satisfaction score (rated from 1 to 10, with higher scores indicating greater life satisfaction) among a sample of college students. They hypothesize that age will predict life satisfaction among college students. Compute an analysis of regression.

F-statistic                             ______

Decision                               ______

10. Suppose that a computer glitch inflated each life satisfaction score by two. Subtract 2 points from each life satisfaction score to correct this. Compute an analysis of regression.

F-statistic                             ______

Decision                               ______

11. Instead, suppose that the computer glitch divided each life satisfaction score by half. Multiply each life satisfaction score by 2 to correct this. Compute an analysis of regression.

F-statistic                             ______

Decision                               ______

12. Does the F-statistic or the decision change from Question 1 to 3? Explain why.

In a study of memory process, rats were first presented with a fear-inducing stimulus on a learning task as soon as they stepped across a line in a test chamber. Afterwards, the rats were divided and given electrical stimulation either 50 or 150 milliseconds after crossing the line. In addition, the rats differed in terms of the area in which the stimulation electrodes were implanted in their brains (Neutral Area, Area A, or Area B). Researchers were interested in the time it took the animals to re-cross the line on a subsequent learning task. The idea is that stimulation of certain areas in the brain would interfere with memory and hence delay learning to avoid the line on the subsequent learning task. The data on time to re-cross the line are below. What can be concluded with an α of 0.05?

                     Area

Time: test statistic =

Area: test statistic =

Interaction: test statistic =

Compute the corresponding effect size(s) and indicate magnitude(s).
Time: η² =   ;  ---Select--- na trivial effect small effect medium effect large effect  
Area: η² =   ;  ---Select--- na trivial effect small effect medium effect large effect  
Interaction: η² =   ;  ---Select--- na trivial effect small effect medium effect large effect  

A) If sample data are such that the null hypothesis is rejected at the alpha=5% level of significance based upon a 2 tailed test, is Ho also rejected at the alpha=1% level of significance? Explain.

B) If a 2 tailed hypothesis test leads to rejection of the null hypothesis at a certain level of significance, would the corresponding 1 tailed test lead to rejection of the null hypothesis? Explain.

1. Describe a scenario where a researcher could use a Goodness of Fit Test to answer a research question. Fully describe the scenario and the variables involved and explain the rationale for your answer. Why is that test appropriate to use?
2. Describe a scenario where a researcher could use a Test for Independence to answer a research question. Fully describe the scenario and the variables involved and explain the rationale for your answer. Why is that test appropriate to use?
3. The Goodness of Fit Test and Test for Independence both use the same formula to calculate chi-square. Why? I.e., explain the logic of the test. (3 points)
4. Compare the Goodness of Fit Test and the Test for Independence in terms of the number of variables and levels of those that can be compared. In what ways are they similar or different?
5. Describe how the Test for Independence and correlation are similar yet different.

True/false. The eval score is a significant predictor of salary at the 5% level.

True

False

It is thought that the mean length of trout in lakes in a certain region is 20 inches. A sample of 46 trout from one particular lake had a sample mean of 18.5 inches and a sample standard deviation of 4 inches. Conduct a hypothesis test at the 0.05 level to see if the average trout length in this lake is less than mu=20 inches.

How do you tell if you can complete a significance test?

Do degrees of freedom apply to dependent observations of data? Pls give sample?

Correlations

1. A correlation is a:

2. A perfect positive correlation of +1.00 means that:

3. A correlation of .00 means that:

4. A correlation of -1.00 means that:

5. The frequencies on a communication task are listed below. The hypothesis being tested is also provided. Fill out the chart below and follow the 12 steps on page 348 to compute the correlation coefficient (r), test r against its critical value at the .05 significance level, answer the hypothesis, and interpret your findings.

H_alt:      When people are giving directions, the number of hand movements will be positively correlated to the number of facial expressions.

1. Step 6:
2. Step 7:
3. Step 8:
4. r =
5. df =
6. Critical r =
7. Interpretation:

From the data collected below, show how you have followed all 14 of the steps on page 340 to compute the chi-square test of difference by completing the information in the charts below. Answer the hypothesis and interpret your findings. You can use the abbreviations provided in the first chart in Labels column of the second chart. For example, reference Japanese individuals who primarily utilized an action-based strategy to resolve a conflict episode as AJ.

1. X²=
2. df =
3. Critical X²=
4. Interpretation =