Appraise what new statistical methods are used in the evaluation of conceptual theories outlining specific advantages these methods provide. Compare Structural Equation Modeling (SEM) techniques providing advantages of using SEM to other conventional methods outlining some of the various statistical techniques that SEM is able to perform. Evaluate sampling techniques used to conduct hypothetical studies and asses the benefits of each sampling method based on best fit to application. Critique validity and reliability methods for appropriate constructs and compare advantages and disadvantages of each method describing what methods to use with different operational techniques. Compare and evaluate factor analysis for confirmatory versus exploratory methods and assess when each is appropriate proving examples and application usages. Assess the differences of various regression analysis methods and demonstrate by examples what regression methods are most appropriate for different application. Finally discuss and recommend best statistical techniques and methods to operationally use for means comparisons, non parametric evaluation, bivariate correlation, ANOVAs, Chi Square, regression, and other techniques as appropriate. Assess the overall concept of statistical power, why it has import to statistical evaluations, and what SPSS contributes to statistical analysis in today’s research.

A supermarket chain analyzed data on sales of a particular brand of snack cracker

at 104 stores for a certain one week period. The analyst decided to build a regresion model to predict the sales of the snack cracker based on the total sales of all brands in the snack cracker category.

b. Is there sufficient evidence at 2.5% significance level to claim that linear

    relationship exists between category sales and cracker sales? Show the

   test, and make the conclusion.

Which probability rule would be used to determine the probability of getting into both your first choice graduate program AND getting an interview at your first choice post-graduation?

Solve for the probability of BOTH events occuring if the probability of getting into your first choice graduate program is estimated to be 25% and getting an interview at your first choice job post-graduation is estimated to be 50%.

If the robt = 0.20 and the df = 70 and the test was two-tailed, what is the rcv ?

Given the values provided in #17, should you reject or fail to reject the null hypothesis?

Significance level is 0.05

Choose the correct answer.

1. What is the percentile rank of 60 in the distribution of N(60, 100)?

a. 10

b. 50

c. 60

d. 100

1. The skewness value for a set of data is +2.75. This indicates that the distribution of scores is which one of the following?

   1. Highly negatively skewed

   2. Slightly negatively skewed

   3. Symmetrical

   4. Slightly positively skewed

   5. Highly negatively skewed

2. For a normal distribution, all percentiles above the 50th must yield positive z-scores. Is this true or false?

3. The distribution of variable X has a mean of 10 and is positively skewed. The distribution of variable Y has the same mean of 10 and is negatively skewed. Are the medians for the two variables the same or different?

A starting lineup in basketball consists of two guards, two forwards, and a center. (a) A certain college team has on its roster four centers, four guards, three forwards, and one individual (X) who can play either guard or forward. How many different starting lineups can be created? [Hint: Consider lineups without X, then lineups with X as guard, then lineups with X as forward.]

(Hypothetical) In a major national survey of crime victimization, the researchers found that 17.0% of Americans age 12 or older had been a victim of crime. The size of the sample was 6,4,00.

a) Estimate the percentage of Americans age 12 or older who were victims at the 95% confidence level. Write a sentence explaining the meaning of this confidence interval.

b) Estimate the percentage of victims at the 99% confidence level. Write a sentence explaining the meaning of this confidence interval.

Imagine that the Sample size was cut in half to 3,200, but the survey found the same value of 17.0% for the percentage of victims.

c) Would the 95% confidence interval increase or decrease? By how much?

d) Would the 99% confidence interval increase or decrease? By how much?

The number of chocolate chips in a bag of chocolate chip cookies is approximately normally distributed with a mean of 1262 chips and a standard deviation of 118 chips.

​(a) Determine the 27th percentile for the number of chocolate chips in a bag. ​

(b) Determine the number of chocolate chips in a bag that make up the middle 98​% of bags. ​

(c) What is the interquartile range of the number of chocolate chips in a bag of chocolate chip​ cookies?

The effectiveness of antidepressants in treating the eating disorder bulimia was examined in the article “Bulimia Treated with Imipramine: A Placebo-Controlled Double-Blind Study” (American Journal of Psychology [1983]: 554–558). A group of patients diagnosed with bulimia were randomly assigned to one of two treatment groups, one receiving imipramine and the other a placebo. One of the variables recorded was binge frequency. The authors chose to analyze the data using a rank-sum test because it makes no assumption of normality. They stated that “because of the wide range of some measures, such as frequency of binges, the rank sum is more appropriate and somewhat more conservative.” Data on number of binges during one week that are consistent with the findings of the article are given in the following table:

Placebo 8 3 15 3 4 10 6 4

Imipramine 2 1 2 7 3 12 1 5

Do these data strongly suggest that imipramine is effective in reducing the mean number of binges per week? Use a level .05 rank-sum test.

There is one 1$ bill and one 5$ bill in your left pocket and three 1$ bills in your right pocket. You move one bill from the left pocket to the right pocket. After that you take one the remaining bill from the left pocket and one of the bills at random from your right pocket. Let ? denote the amount of money that you take from the left pocket and ? denote the amount of money that you take from the right pocket.

1. ? (?=1, ? =1) is

(a) 1

(b) 3 (correct)

(c) 1

(d) 5

2. ? (?=5, ? =5) is

(a) 0 (correct)

(b) 1/8

(c) 3/8

(d) 1/2

3. ?(? ≥?)is
(a) 1/8

(b) 3/8

(c) 1/2 (correct)

(d) 1

4. Covariance between ? and ? is

(a) 0

(b) −1/2

(c) −1 (correct)

(d) 1

5. Let ? denote the total amount of money that you get from your pockets. V??(?) is

(a) 23/4

(b) 31/8

(c) 19/4

(d) 15/4 (correct)

6. Let ? denote the share of money that you get from the left pocket, i.e. ?/? . Calculate the mean of ?
(a) 1/2

(b) 2/3

(c) 11/13

(d) 5/8 (correct)

An academic department has just completed voting by secret ballot for a department head. The ballot box contains four slips with votes for candidate A and three slips with votes for candidate B. Suppose these slips are removed from the box one by one. For example, one outcome is BBBAAAA. (Enter your answers in set notation. Enter EMPTY or ∅ for the empty set.) (a) List all possible outcomes. This answer has not been graded yet. (b) Suppose a running tally is kept as slips are removed. For what outcomes does A remain ahead of B throughout the tally?

consider the following numbers: -5,-3,-1,1,3. assuming that these numbers are the sample data, use a pencil and calculator to calculate the mean, standard deviation and variance. please show work

what is the average age in the class? what is the average feeling? what is the average city?

Each front tire on a particular type of vehicle is supposed to be filled to a pressure of 26 psi. Suppose the actual air pressure in each tire is a random variable. X for the right tire and Y for the left tire, with joint pdf.

f(x,y) = k(x² + y²), when 20 ≤ x ≤ 30, 20 ≤ y ≤ 30, and

f(x,y) = 0 (otherwise)

A. What is the value of k.

B. what is the probability that both tires are underfilled?

C. What is the marginal distribution of air pressure in the right tire?

Let X be a uniform random variable with pdf f(x) = λe−λx for x > 0, and cumulative distribution function F(x).

(a) Show that F(x) = 1−e −λx for x > 0, and show that this function satisfies the requirements of a cdf (state what these are, and show that they are met). [4 marks]

(b) Draw f(x) and F(x) in separate graphs. Define, and identify F(x) in the graph of f(x), and vice versa. [Hint: write the mathematical relationships, and show graphically what the functions represent.] [4 marks]

(c) X has mgf M(t) = λ(λ−t) −1 . Derive the mean of the random variable from first principles (i.e. using the pdf and the definition of expectation). Also show how this mean can be obtained from the moment generating function. [10 marks]

(d)

(i) Show that F −1 (x) = − 1 λ ln(1 − x) for 0 < x < 1, where ln(x) is the natural logarithm. [4 marks]

(ii) If 0 < p < 1, solve F(xp) = p for xp, and explain what xp represents. [4 marks] (iii) If U ∼ U(0, 1) is a uniform random variable with cdf FU (x) = x (for 0 < x < 1), prove that X = − 1 λ ln(1 − U) is exponential with parameter λ. Hence, describe how observations of X can be simulated. [4 marks]

Suppose men's heights are normally distributed with mean of 176 cm and variance of 25cm^2.

A. What proportion of mean are between 172 cm and 178 cm tall?

B. Find the minimum ceiling of an airplane such that at most 2% of the men walking down the aisle will have to duck their heads.

C. Suppose you take a random sample of 6 men. What is the sampling distribution of the sample mean height? Why?

D. Find the probability that the average height of a random sample of 64 men is greater than 178cm. If these heights were not normally distributed, would you still be able to answer the question? why or why not?