Problem Set 3: One-Way randomized ANOVA

Research Scenario: A health psychologist is looking into the effects of different kinds of exercise on stress. She divides volunteers into three exercise groups: high-intensity interval training (HIIT) (n=8), yoga (n=8), or running (n=8). The volunteers participate in a set number of hours of the exercise for a month, after which the psychologist measures their stress levels on a scale of 1-40 where lower scores = lower stress, and higher scores = higher stress. The scores for each group are shown in the table below. Input the data into SPSS (remember you will enter the data only using 2 columns - one for group (make sure you label the values) and one fore stress. Conduct a one-way ANOVA to determine the effect of these different exercises on stress levels.

11) Paste relevant SPSS output

12) Create an appropriate graph to display this data.

13) Write an APA-style Results section based on your analysis. All homework "Results sections" should follow the examples provided in the presentations and textbooks. They should include the statistical statement within a complete sentence that mentions the type of test conducted, whether the test was significant, and if relevant, effect size and/or post hoc analyses. Don't forget to include a decision about the null hypothesis.

Fully describe how to use the unified approach for a Poisson distribution describing signal and background events. Illustrate this by constructing a 90% confidence level interval for the number of observed events given a signal yield µ of 2 events and an assumed background of 1 events. You may wish to consider total event yields between zero and ten.

(a) Use Excel, MegaStat, or MINITAB to fit three trends (linear, quadratic, exponential) to the time series. (A negative value should be indicated by a minus sign. Do not round the intermediate calculations. Round your final answers to 2 decimal places.)

(b) Use each of the three fitted trend equations to make numerical forecasts for the next 3 years. (Round the intermediate calculations to 2 decimal places and round your final answers to 1 decimal place.)

T Linear| Exponential | Quadratic

9 _________ _________ _________

10 _________ _________ _________

11 _________ ___________ _________

Why are sampling distributions important to the study of inferential statistics? In your answer, demonstrate your understanding by providing an example of a sampling distribution from an area such as business, sports, medicine, social science, or another area with which you are familiar. Remember to cite your resources and use your own words in your explanation.

(NO PICTURES PLEASE! Text only)

Let (X_1, ..., X_k) be a multinomial distribution with probabilities p_1, ..., p_k in n independent trials. Calculate E(X_i), and COV(X_i, X_j) for 1 <= i, j <= k.

3. [10 marks] A sample survey of 54 discount brokers showed that the mean price charged for a

trade of 100 shares at $50 per share was $33.77 and a sample standard deviation of $15.

a.    [3] Develop a 95% confidence interval for the mean price charged by discount brokers for a trade of 100 shares at $50 per share.

b.    [2] Explain, in context, what the interval you found tells you.

c.     [3] What sample size would be necessary to achieve a margin of error of $2? Assume a

confidence level of 95%.

d.    [2] Three years ago the mean price charged for a trade of 100 shares at $50 per share was

$39.25. Has the price dropped significantly? Justify.

You wish to test the following claim ( H a ) at a significance level of α = 0.002 . H o : p 1 = p 2 H a : p 1 > p 2 You obtain 86.6% successes in a sample of size n 1 = 732 from the first population. You obtain 79% successes in a sample of size n 2 = 395 from the second population. For this test, you should NOT use the continuity correction, and you should use the normal distribution as an approximation for the binomial distribution.
ALL I NEED IS FOR SOMEONE TO SHOW ME HOW TO INPUTE THIS ON A CALCULATOR TI 84...the 2-PropZ TEST doesnt accept decimals.

In a recent Super Bowl, a TV network predicted that 39 % of the audience would express an interest in seeing one of its forthcoming television shows. The network ran commercials for these shows during the Super Bowl. The day after the Super Bowl, and Advertising Group sampled 105 people who saw the commercials and found that 40 of them said they would watch one of the television shows. Suppose you are have the following null and alternative hypotheses for a test you are running: H 0 : p = 0.39 H a : p > 0.39

To identify regional groupings of market segments it is useful to use which of the following research tools? Select one: a. Cluster analysis b. Factor analysis c. Simple random sampling d. Open-ended questions

The following marketing research technique(s) is used for perceptual mapping: Select one: a. correlation and regression b. conjoint analysis c. t-tests and ANOVA d. multidimensional scaling

Toyota company prides themselves on customer service. they have been trying to determine exactly how long it takes, from start to finish, to buy a car at their dealerships. they have determined that the two parts of the transaction (showroom and service) follow the normal model. showroom has a mean time of 3.5 hours with a standard deviation of 1.5 hours. service has an average time of 2 hours with a standard deviation of 0.5 hours.

a) What is the mean and standard deviation of the difference between the showroom and service average waiting time.

b) What is the probability that it will take a customer longer during the service portion of the transaction.

c) Why does the standard deviation always increase when we add or subtract the means of two distributions.

There are 3 SPSS outputs in this homework assignment. The questions for each output are listed below. Please type your answers into this word document and submit it as an attachment in the assignment tab.

Q1. Researchers were interested in determining whether background music helped or hindered students’ performance on a math test. Students were randomly assigned to 1 of 3 groups: 1) no music; 2) music only; and 3) music with lyrics. Students were then given a math exam, scores which could range from 0 to 100.

1. State the null and alternate hypotheses.
2. What is the total sample size
3. Identify the independent and dependent variables
4. What is the test statistic value
5. What is the p value
6. What is your conclusion (assume α = .05). Phrase your conclusion based on your hypotheses.
7. Do we need a post hoc analysis Why or why not

2. An experiment was conducted by a physiologist to determine whether exercise improves the human immune system. Thirty subjects volunteered to participate in the study. The amount of immunoglobulin known as IgG (an indicator of long-term immunity) and the maximal oxygen uptake (a measure of aerobic fitness level) were recorded for each subject. The data can be found in the file marked AEROBIC. You will need to use the Data Analysis - Regression Function for this problem, as well as some graphing functions.

a. Construct a scattergram for the IgG-maximal oxygen uptake data.

b. Hypothesize a probabilistic model relating IgG to maximal oxygen uptake.

c. Fit the model to the data. Is there sufficient evidence to indicate that the model provides information for the prediction of IgG, y? Test using α = .05.

d. Does a second-order term contribute information for the prediction of y? Test using α = .05.

Use the table below to answer questions 4.5 – 4.7: This table contains the same client data as the first table. This time, though, the instructor is interested in knowing how his clients’ other activities might impact their average cycling speed in spin class. He notes that half of his clients also ride bikes outside during the week, while the other half of his clients do not bike anywhere except spin class.

Average Speed M = 19 M = 17

4.5 Calculate SS for each sample of spin class clients (the portion who ride outside and the portion who only do spin class). Show Work by inserting numbers into the table to show intermediate steps Rides Outside SS = Only Spin Class SS =

4.6 Calculate s for each group Rides Outside s = Only Spin Class s =

4.7 Based on the statistics you have computed, does there appear to be any difference in average speed between those who bike outside and those who only bike during spin class?

Explain why or why not?

What effect do nutrient additions have on plant species diversity? Long-term experiments at the Rothamstead Experimental Station in the U.K. sought to investigate the relationship, with some interesting findings.

The data can be found in the linked Google Sheets document  - you'll want to copy it to Excel and use the Data Analysis ToolPak.

1) Produce a scatter plot of the data (click here for a generic youtube video on creating a scatter plot from excel data - this is for informational purposes only - it's not your data)

• Which is the explanatory variable? (nutrients OR species)
• Which is the response variable? (nutrients OR species)
• Looking at your scatter plot, do you observe a positive or negative relationship?  

2) Add the least-squares regression line to your scatter plot. (click here for a generic youtube video on adding trendlines to scatter plots - this is for informational purposes only - it's not your data)

• What fraction of the variation in the number of plant species is "explained" by the number of nutrients added? Answer to two decimal places.

3) Test the hypothesis of no treatment effect on the number of plant species.

• What is your t-value?  
• Do you accept or reject the null hypothesis?

A physician with a practice is currently serving 280 patients. The physician would like to administer a survey to his patients to measure their satisfaction level with his practice. A random sample of 22 patients had an average satisfaction score of 8.3 on a scale of​ 1-10. The sample standard deviation was 1.3 . Complete parts a and b below. a. Construct a​ 99% confidence interval to estimate the average satisfaction score for the​ physician's practice. The​ 99% confidence interval to estimate the average satisfaction score is left parenthesis nothing comma nothing right parenthesis . ​(Round to two decimal places as​ needed.)