Please correct chosen answers if incorrect.

22) d

23) c

24) c

22) Which of the following is not true regarding event rates:

a. an event can be anything such as Chicago Cubs winning the World Series

b. event rates are seldom used as they only provide data of nominal significance

c. event rate is statistical term that describes how often an event occurs

d. the formula for event rate is the number of times the event occurs, divided by the number of possible times the event could occur

23) Which of the following statements is not true regarding data collection:

a. often times, in our field, we collect data to help us infer or hypothesize about any number of things including treatments, prevention, occurrences, etc

b. collecting count data may be on one single sample or cohort, due to any number of reasons

c. when data is collected on count data, e call the outcome of that collection, results

. in single group studies, control groups are the standard

24) Which of the following statements is true:

a. comparisons between age-adjusted rates can only be useful if the same standard population is used in the creation of the age-adjusted rates

b. event rates are never seen as something which is important in public health except in epidemiological concerns

c. count data is something that is important when considering data gathered on vampires

d. person-time is often used in epidemiological studies in the veterinary sciences

Dole Pineapple Inc. is concerned that the 16-ounce can of sliced pineapple is being overfilled. Assume the population standard deviation of the process is .04 ounce. The quality control department took a random sample of 60 cans and found that the arithmetic mean weight was 16.05 ounces. At the 3% level of significance (Step 2), can we conclude that the mean weight is greater than 16 ounces?

Step 1: State the null hypothesis (H0) and the alternate hypothesis (H1). (insert >, >, =,< or <) where appropriate. Ho:  ______ 16 H1:  _______16

Step 2: you select the level of significance, =.03 (Given in problem description)

Step 3: Identify the test statistic (circle ‘t distribution’ or ‘Normal Curve (z)’) use the t distribution or Normal Curve (z)

Step 4: Formulate the decision rule Reject Ho if _______________________

Step 5: Take a sample arrive at a decision

Step 6: Interpret the results (circle ‘Reject’ or ‘Accept’) circle ‘are’ or ‘are not’) Reject or Accept Ho. The cans are or are not being overfilled.

Please show legible work!

An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 150 engines and the mean pressure was 4.0 pounds/square inch (psi). Assume the population standard deviation is 0.7 . If the valve was designed to produce a mean pressure of 4.1 psi, is there sufficient evidence at the 0.05 level that the valve does not perform to the specifications? is there sufficient or not sufficient evidence?

Find the following probabilities.

A.) P(X=5), X FOLLOWING A BINOMIAL DISTRIBUTION, WITH N=50 AND P=.7.

B.) P(X = 5), X following a Uniform distribution on the interval [3,7].

c.) P(X = 5), X following a Normal distribution, with µ = 3, and σ = .7.

(To complete successfully this homework on Stochastic Models, you need to use one of the software tools: Excel, SPSS or Mathematica, to answer the following items, and print out your results directly from the software. )

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.

HIIT	16	25	19	11	17	11	15	27
YOGA	19	21	22	23	14	24	27	15
RUNNING	19	28	33	24	26	30	17	21

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.

Number of Certified Organic Farms in the United States, 2001–2008
Year	Farms
2001	6,375
2002	6,730
2003	7,441
2004	7,425
2005	7,882
2006	8,758
2007	10,297
2008	12,019

(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.)

Linear	yt = ____ xt + ______
Quadratic	yt = ____ xt2 +_____ xt + _____
Exponential	yt = _____ e ____x

(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

	N	Mean	Std. Deviation	Std. Error	95% Confidence Interval for Mean
					Lower Bound	Upper Bound
No music	250	77.59	13.055	.826	75.96	79.21
Music only	250	78.10	13.357	.845	76.44	79.77
Music and lyrics	250	78.97	13.263	.839	77.32	80.62
Total	750	78.22	13.221	.483	77.27	79.17

ANOVA
minutes
	Sum of Squares	df	Mean Square	F	Sig.
Between Groups	244.595	2	122.297	.699	.497
Within Groups	130668.664	747	174.925
Total	130913.259	749