A study was done on body temperatures of men and women. The results are shown in the table. Assume that the two samples are independent simple random samples selected from normally distributed​ populations, and do not assume that the population standard deviations are equal. Complete parts​ (a) and​ (b) below. Use a 0.01 significance level for both parts.

Men                 Women

μ          μ1                    μ2

n          11                    59

x          97.78°F           97.25°F

s           0.97°F             0.66°F

a. Test the claim that men have a higher mean body temperature than women.

What are the null and alternative​ hypotheses?

A. H0​: μ1≥μ2

H1​: μ1<μ2

B. H0​: μ1=μ2

H1​: μ1≠μ2

C. H0​: μ1=μ2

H1​: μ1>μ2

D. H0​: μ1≠μ2

H1​: μ1<μ2

The test​ statistic, t, is _____. ​(Round to two decimal places as​ needed.)

The​ P-value is _____. ​(Round to three decimal places as​ needed.)

State the conclusion for the test.

A. Reject the null hypothesis. There is not sufficient evidence to support the claim that men have a higher mean body temperature than women.

B. Fail to reject the null hypothesis. There is not sufficient evidence to support the claim that men have a higher mean body temperature than women.

C. Reject the null hypothesis. There is sufficient evidence to support the claim that men have a higher mean body temperature than women.

D. Fail to reject the null hypothesis. There is sufficient evidence to support the claim that men have a higher mean body temperature than women.

b. Construct a confidence interval suitable for testing the claim that men have a higher mean body temperature than women.

_____<μ1−μ2<_____ ​(Round to three decimal places as​ needed.)

You download two sets of posts from an online forum. Set One is a collection of posts by "pro-Hong Kong Protestors" (HKP) students. Set Two is a collection of posts by pro-Chinese Government (CG) students. (Let's say you get these two collections by searching for students who are members either of a pro-HKP group, or pro-CG group.) You compute the probabilities of different words they use, and focus on a set of six "key" words of interest, {"legal", "democracy", "violence", "legitimate", "calm", "foreign"}. You compute the "probability that, given that they use one of these five words, which word it is" (you could do this by counting up each of those words for the two sets, and dividing by the total number of those words in each set.) words: {"legal", "democracy", "violence", "legitimate", "calm", "foreign"}. pHKP = {0.2, 0.2, 0.3, 0.2, 0.05, 0.05} pCG = {0.1, 0.05, 0.3, 0.05, 0.1, 0.4}

The government tells you that they think about 10% of the posters on the mainland are pro-HKP, and they just want to have a conversation with these people about things.

You encounter a post. The poster uses the word "democracy" twice, the word "violence" once, and the word "foreign" once. Assuming that he is either pro-HKP, and follows the pHKP distribution, or pro-CG, and follows the pCG distribution...

Q: Given government priors, what is the probability that the poster is pro-HKP? (i.e., follows the pHKP distribution rather than the pCG distribution)

Use the Multiplication Rule to find the number of positive divisors of 20!. Include a procedure that “builds” such divisors

Suppose that a company's sales increase when the economy is doing well. Also, suppose that the
company's advertising budget is based upon the number of sales, and that larger sales lead to a larger
advertising budget.
A There is an association between how well the economy is doing and the company's advertising budget.
B There is a causal relationship between the company's sales and the company's advertising budget.
C Both of the above.
D Neither of the above.

Project Assignment The purpose of this assignment is for you to gain practice in applying the concepts and techniques we learned in class. In order to complete the assignment, please do the following:

1. find or create a data set containing values of at least one interval or ratio variable for at least one-hundred cases (n >= 100); 1

2. provide basic descriptive statistics to summarize the central tendency and variability of the data;

3. provide at least one table (see chapter 2: frequency, percentage, cumulative frequency, or cumulative percentage) summarizing the distribution of the data;

4. provide a graph (see chapter 3: histogram, line graph, or time series graph) that illustrates a salient or important property or set of properties of the data;

5. calculate a confidence interval for the value of the variable; and

6. conduct a hypothesis test using the data.

Write a short paper (~2-4 pages double spaced) summarizing your work. Be sure to clearly describe your findings, why you chose to analyze the data as you did, and what your results mean. For example, if you chose to summarize the data’s variability using the interquartile range (as opposed to the standard deviation), explain why you made this choice. Be sure to be as specific and clear as possible about the rationale underlying your choices and about your findings.

1 Note that projects analyzing a nominal or ordinal variable will receive no credit (i.e., a grade of zero).

You are a cognitive psychologist who has developed a new treatment for depression. Currently, the most effective treatments for depression are behavioral treatments and pharmacological treatments (treatments involving medication). In order to validate your new treatment, you need to show that it is at least as effective as behavioral treatment and medication. You conduct a clinical trial to determine the effectiveness of your treatment by randomly assigning 60 individuals with depression to four treatment groups: a Control group (n = 15), a Cognitive Therapy group (n = 15), a Behavioral Therapy group (n = 15), and a Pharmacological Therapy group (n = 15). After 6 weeks of treatment, you assess depression using the Beck Depression Inventory (BDI; range: 0 – 63 with 0 indicating no depression and 63 indicating severe depression). Use the 6 steps of hypothesis testing and SPSS to determine whether the groups differ in terms of scores on the BDI. Use the SPSS #2 to conduct the statistical test, record your answers on the answer sheet and attach SPSS output.

a) What is the appropriate statistical test to answer question? (0.5 pt)

b) Step 1: What is your prediction regarding the results of the statistical test? (0.5 pt)

c) Step 2: Set up hypotheses (2 pts)

H₀ (1 pt):
H₁ (1 pt):   

d) Step 3: Set criteria for decision (2 pts)

Critical value (1 pt):
Decision Rule (1 pt):   

e) Step 5: Report Results (2 pts) – Must include test statistic (0.5 pts), degrees of freedom (0.5 pts), p-value (0.5 pts), and appropriate measure of effect size (0.5 pts)

f) Post-hoc comparisons (1 pt) – Conduct Tukey’s HSD and report differences between groups by using “>”, “<”, or “=” to demonstrate which group’s mean is greater than the other (The first two have been filled out as a guide).

g) Step 6: Interpret the results of the statistical test in terms of the research question (1 pt)

SPSS DATA
Control   74
Control   70
Control   83
Control   66
Control   90
Control   97
Control   104
Control   100
Control   75
Control   92
Control   89
Control   70
Control   83
Control   95
Control   108
Pharmacological Therapy   79
Pharmacological Therapy   89
Pharmacological Therapy   89
Pharmacological Therapy   75
Pharmacological Therapy   67
Pharmacological Therapy   74
Pharmacological Therapy   90
Pharmacological Therapy   81
Pharmacological Therapy   65
Pharmacological Therapy   68
Pharmacological Therapy   85
Pharmacological Therapy   71
Pharmacological Therapy   69
Pharmacological Therapy   67
Pharmacological Therapy   70
Behavioral Therapy   44
Behavioral Therapy   68
Behavioral Therapy   71
Behavioral Therapy   35
Behavioral Therapy   62
Behavioral Therapy   65
Behavioral Therapy   70
Behavioral Therapy   65
Behavioral Therapy   45
Behavioral Therapy   41
Behavioral Therapy   46
Behavioral Therapy   68
Behavioral Therapy   69
Behavioral Therapy   39
Behavioral Therapy   42
Cognitive Therapy   55
Cognitive Therapy   48
Cognitive Therapy   64
Cognitive Therapy   40
Cognitive Therapy   30
Cognitive Therapy   31
Cognitive Therapy   63
Cognitive Therapy   30
Cognitive Therapy   64
Cognitive Therapy   69
Cognitive Therapy   45
Cognitive Therapy   39
Cognitive Therapy   31
Cognitive Therapy   66
Cognitive Therapy   36

****ANSWERS ARE GIVEN BUT MUST SHOW ALL WORK; PLEASE (NO EXCEL OR SPSS)*****

----------------------------------------------------------------------

1. To answer this question, refer to the following hypothetical data collected using replicated measures design.

A. In a two-tailed test of H 0 using α=0.05, what is p(obtained) for the results shown? *Hint: "two-tailed" means the same thing as nondirectional. ANSWER = 0.0216

B. What would you conclude regarding H0 using a = 0.05 2-tail? ANSWER = Since the p-value (0.0216) < α=0.05, we reject the null hypothesis H

----------------------------------------------------------------------

2. Conduct a one-way ANOVA on the following data.

What is your conclusion (use an alpha)? ANSWER= Reject H0

----------------------------------------------------------------------

3. Given the following data:

A) What is the value of F crit for the column effect (variable b ) *Hint: don't forget to evaluate a numerator (for variable B and denominator df within) ANSWER = 3.40

B) Given the following data, what is the value of the SS total? ANSWER = 121.8667

Consider a six-sided fair dice. Complete the following tables for this die:

This is the entire question, does not say how many times the dice is thrown

question13: TABLE 14-1

A manager of a product sales group believes the number of sales made by an employee ( Y) depends on how many years that employee has been with the company ( X ₁) and how he/she scored on a business aptitude test ( X ₂). A random sample of 8 employees provides the following:

Referring to Table 14-1, for these data, what is the estimated coefficient for the variable representing scores on the aptitude test?

question 14:

TABLE 14-1

A manager of a product sales group believes the number of sales made by an employee ( Y) depends on how many years that employee has been with the company ( X ₁) and how he/she scored on a business aptitude test ( X ₂). A random sample of 8 employees provides the following:

Referring to Table 14-1, if an employee who had been with the company 5 years scored a 9 on the aptitude test, what would his estimated expected sales be?

A person's blood glucose level and diabetes are closely related. Let x be a random variable measured in milligrams of glucose per deciliter (1/10 of a liter) of blood. Suppose that after a 12-hour fast, the random variable x will have a distribution that is approximately normal with mean μ = 90 and standard deviation σ = 24. Note: After 50 years of age, both the mean and standard deviation tend to increase. For an adult (under 50) after a 12-hour fast, find the following probabilities. (Round your answers to four decimal places.)
(a) x is more than 60


(b) x is less than 110


(c) x is between 60 and 110


(d) x is greater than 125 (borderline diabetes starts at 125)

The table below contains the overall miles per gallon​ (MPG) of a type of vehicle.

Construct a 95​% confidence interval estimate for the population mean MPG for this type of​ vehicle, assuming a normal distribution.The 95​% confidence interval estimate is from ____ MPG to ____ MPG.

​(Round to one decimal place as​ needed.)

A bridge across a deep jorge has a capacity of 5184 pound. If the weights of tourists have a mean of 160 pounds and a standard deviation of 38 pounds, find the probability that a group of 32 not-overly-bright tourists who attempts to cross the gorge simultaneously will plummet to a grisly death. (Hint: the groups weight will exceed 5184 pounds if the mean weight in the group is over 162 pounds)

An airline records flight delays in and out of Chicago O'Hare airport for a year. The average delay for these flights is 12.66 minutes with a standard deviation of 4.17 minutes. For a sample of 77 flights, 91% of flights will have an average delay less than how many minutes?

Question 3 options:

Learning Objectives

1. Learn more about the statistical analysis tools in SPSS.
2. Practice manual calculations and confirm with SPSS output.
3. Walk through all steps of hypothesis testing for a related-samples t-Test.

About Your Data

A statistics student was late on completing the final statistics project. While racking her brain for ideas, she watched her cat eating supper and noticed how much quicker the cat ate the new brand of cat food. Feeling desperate about the project, she decided to figure out if cats really do prefer Brand A over Brand B. She catnapped six neighborhood cats (No judging!) and deprived them of food for 10 hours. Then she gave the cats Brand A, measured the amount of food eaten, deprived them of food for another 10 hours and gave them Brand B. The amounts eaten in grams are listed below:

Instructions

The steps below are slightly different from the ones laid out by your textbook author. I want you to follow my six steps below. Also, because it can be difficult and time consuming trying to figure out how to insert symbols into a word processing document, I would like you to complete your manual work with pencil and paper.

Six Steps of Hypo Testing and Manual Calculations

You will be conducting a related-samples t-Test (SPSS calls it a Paired-Samples test) to determine whether the cats have equal preference for Brands A and B. Your alpha level will be .05.

Write out your six steps for this ethically dubious though highly entertaining study. ;-)

1) State H₀ using symbols AND words
2) State H₁ using symbols AND words
3) State your alpha level
4) Articulate your rejection rule ("Reject H₀ if |obtained t| ≥ critical t, t_crit = _____")
5) Manually calculate your related-samples t value (Show your work. Carry your calculations out to two decimal places. Feel free to calculate standard deviation on calculator.)
6) State your conclusions in four parts. a. What did you do? b. What did you find? c. What does it mean? d. What can we do with these findings? (REFER BACK TO ABOVE VIDEO for explanation and examples of the different parts of Step 6. Follow the template provided in the video.)

Effect-Size Statistics

What are Cohen's d and the confidence interval of the difference? The confidence interval is listed in the SPSS output. You can do a quick internet search for "Cohen's d" calculator and find many websites that will allow you to quickly perform that calculation. Once you have your effect sizes, explain what they mean.

Decision-Making Errors

Of course, there is always the possibility of Type I or Type II error. Which type of error is relevant in this case? What are some possible consequences of this type of error?