1. Imagine a study that indicates that patients given arthroscopic debridement, arthroscopic lavage or a placebo surgery all fared equally well in terms of pain and mobility over the next two years. If, in reality, the debridement treatment generally improves performance, what type of error did they make in their conclusion?

(A) Conservative error.

(B) Liberal error.

(C) p value error.

(D) Type I error.

(E) Type II error

2. The F ratio test for equality of variances is not a great test to perform if you are genuinely concerned about the accuracy of your result (i.e., you should use better tests such as the Levene's test instead). The main weakness of the F ratio test is when which of the following is true?

(A) When the data sets are not normally distributed.

(B) When the means are very different.

(C) When the sample sizes are not equal.

(E) When the sample sizes are very large.

(E) When the variances are not equal.

3. Imagine that you collect length (i.e., SVL) data for mice from two different regions. The mice from the forest have a mean SVL of 8.9 cm whereas the mice from the fields have a mean SVL mean of 9.3 cm. If you perform a two-tailed heteroscedastic t test and the overall degrees of freedom are 23 and you obtain a t value of 1.92, what would your best conclusion be?

(A) The mice from the forest are not significantly different from the mice from the fields (0.05 < p < 0.1).

(B) The mice from the forest are significantly different from the mice from the fields (0.025 < p , 0.05).

(C) The mice from the forest are significantly different from the mice from the fields (0.05 < p < 0.1).

(D) The mice from the forest are significantly smaller from the mice from the fields (0.025 < p , 0.05).

(E) The mice from the forest are significantly smaller from the mice from the fields (0.05 < p < 0.1).

4. A researcher assumes that the mean number of red blood cells per ml of blood she collects will be 5,000,000. If she gathers several samples and conducts a two-tailed one-sample t test and obtains a mean value of 5,250,300 and a p value of 0.08, what would her best conclusion be?

(A) Her data indicates that the mean number of blood cells is different from 5,000,000.

(B) Her data indicates that the mean number of blood cells is similar to 5,000,000.

(C) She lacks convincing evidence to decide that the mean number of blood cells is different from 5,000,000.

(D) She lacks convincing evidence to decide that the mean number of blood cells is similar to 5,000,000.

(E) She may have made a type I error.

5. If you are using a table of critical t values and you accidentally use the values for more degrees of freedom than you really have which of these is true?

(A) The risk of making a type I error is increased and the risk of type II error is increased.

(B) The risk of making a type I error is increased and the risk of type II error is decreased.

(C) The risk of making a type I error is decreased and the risk of type II error is increased.

(D) The risk of making a type I error is decreased and the risk of type II error is decreased.

(E) The risk of making a type I error is the same and the risk of type II error is the same.

6. The best description of what a p value represents is which of the following?

(A) The probability that the null hypothesis is true.

(B) The probability of seeing the sample data if the null hypothesis is true.

(C) The probability of seeing the sample data if the null hypothesis is false.

(D) The probability of seeing the sample data if the alternative hypothesis is true.

(E) The probability of seeing the sample data if the alternative hypothesis is false.

7. For a given difference between two sample means, the p value associated with that difference does which of the following?

(A) Decreases as the sample sizes increase and decreases as the sample variances decrease.

(B) Decreases as the sample sizes increase and increases as the sample variances decrease.

(C) Increases as the sample sizes increase and decreases as the sample variances decrease.

(D) Depends on the sample sizes, not the sample variances.

(E) Depends on the sample variances, not the sample sizes.

8. A researcher is interested in whether a drug alters the pH of blood in users. She takes blood samples from a set of individuals before and after taking the experimental medication. Unfortunately, a small number of the sample jar labels got switched and she cannot guarantee which samples are from the same individuals in a few cases. What option below is the most correct?

(A) Because only a few labels are incorrect she can still do a paired t test, she should just use a smaller p value in her analysis.

(B) She cannot do a paired t test, but since the same people are in both samples she can analyze the data with a homoscedastic t test.

(C) She cannot do a paired t test, but she can analyze the data with a heteroscedastic t test.

(D) She cannot do a t test, but she can analyze the data with an F ratio test to answer her overall question.

(E) Since the labels are not correct she cannot do a paired t test and she needs to redo the whole experiment.

9. If the standard error of a sample is 12 and the sample size was 8, which of the following values is closest to the variance of the sample?

(A) 34

(B) 96

(C) 768

(D) 1152

(E) 9216

10. When researchers compare two distributions, they sometimes conduct a Kolmogorov–Smirnov "goodness of fit" test. In this test they calculate a value D which they then compare to critical K values from the Kolmogorov distribution based upon stochastic Brownian processes. If such a test is done and a p value obtained, which of the following is the best description of what that p value represents?

(A) p is the probability that K > D.

(B) p is the probability that the observed sample means would be that different, due to sampling error, when the sample means are really the same.

(C) p is the probability that the D value would be that large if the only observed differences between the sample distributions are due to sampling error.

(D) p is the probability that sampling error causes the sample value of D to be outside the confidence interval for K.

(E) p is the probability that the two distributions are statistically significant.

The variable smokes is a binary variable equal to one if a person smokes and zero otherwise. Cigprice is the price of cigarettes, white is a dummy variable that takes the value 1 if the person is white and 0 otherwise and restaurn is a dummy that takes the value 1 if the person lives in a state with restaurant smoking restrictions.

The estimated linear probability model is

smokes = .656 - .069 log(cigpric) + .012 log(income) - .029 educ + .02 age - .00026 age^2 - .101 restaurn - .026 white

If education increases by four years, what is the effect on the estimated probability of smoking?

The probability of smoking increases by .116 (or 11.6 percentage points)

The probability of smoking decreases by .116 (or 11.6 percentage points)

The probability of smoking decreases by 11.6 (or 11.6 percentage points)

The probability of smoking decreases by .413 (or 41.3 percentage points)

The variable smokes is a binary variable equal to one if a person smokes and zero otherwise. Cigprice is the price of cigarettes, white is a dummy variable that takes the value 1 if the person is white and 0 otherwise and restaurn is a dummy that takes the value 1 if the person lives in a state with restaurant smoking restrictions.

The estimated linear probability model is

smokes = .656 - .069 log(cigpric) + .012 log(income) - .029 educ + .02 age - .00026 age^2 - .101 restaurn - .026 white

At what point does another year of age reduce the probability of smoking?

19

21.93

38.46

51.62

The variable smokes is a binary variable equal to one if a person smokes and zero otherwise. Cigprice is the price of cigarettes, white is a dummy variable that takes the value 1 if the person is white and 0 otherwise and restaurn is a dummy that takes the value 1 if the person lives in a state with restaurant smoking restrictions.

The estimated linear probability model is

smokes = .656 - .069 log(cigpric) + .012 log(income) - .029 educ + .02 age - .00026 age^2 - .101 restaurn - .026 white

Interpret the coefficient of the binary variable “restaurn”

A person who lives in a state with restaurant smoking restrictions has a probability of smoking 10.1 percentage points lower than somebody living in a state without restaurant smoking restrictions

A person who lives in a state with restaurant smoking restrictions has a probability of smoking 10.1 percentage points higher than somebody living in a state without restaurant smoking restrictions

A person who lives in a state with restaurant smoking restrictions has a probability of smoking .101 percentage points lower than somebody living in a state without restaurant smoking restrictions

A person who lives in a state with restaurant smoking restrictions has a probability of smoking 1.01 percentage points lower than somebody living in a state without restaurant smoking restrictions

The variable smokes is a binary variable equal to one if a person smokes and zero otherwise. Cigprice is the price of cigarettes, white is a dummy variable that takes the value 1 if the person is white and 0 otherwise and restaurn is a dummy that takes the value 1 if the person lives in a state with restaurant smoking restrictions.

The estimated linear probability model is

smokes = .656 - .069 log(cigpric) + .012 log(income) - .029 educ + .02 age - .00026 age^2 - .101 restaurn - .026 white

Person number 206 in the datset has cigpric = 67.44, income = 6500, educ =16, age =77, restaurn = 0 and white = 0. What is the predicted probability of smoking?

.12

.65

.053

.0052

The variable smokes is a binary variable equal to one if a person smokes and zero otherwise. Cigprice is the price of cigarettes, white is a dummy variable that takes the value 1 if the person is white and 0 otherwise and restaurn is a dummy that takes the value 1 if the person lives in a state with restaurant smoking restrictions.

The estimated linear probability model is

smokes = .656 - .069 log(cigpric) + .012 log(income) - .029 educ + .02 age - .00026 age^2 - .101 restaurn - .026 white

What is the interpretation of the coefficient for log(cigpric)?

If cigarette prices go up 1% then the probability of smoking decreases by .00069 (or .069 percentage points)

If cigarette prices go up 1% then the probability of smoking increases by .00069 (or .069 percentage points)

If cigarette prices go up 1% then the probability of smoking decreases by .69 (or 6.9 percentage points)

If cigarette prices go up 1% then the probability of smoking decreases by 6.9 (or 69 percentage points)

The variable smokes is a binary variable equal to one if a person smokes and zero otherwise. Cigprice is the price of cigarettes, white is a dummy variable that takes the value 1 if the person is white and 0 otherwise and restaurn is a dummy that takes the value 1 if the person lives in a state with restaurant smoking restrictions.

The estimated linear probability model is

smokes = .656 - .069 log(cigpric) + .012 log(income) - .029 educ + .02 age - .00026 age^2 - .101 restaurn - .026 white

What is the interpretation of the coefficient for log(income)?

If income goes up 1% then the probability of smoking increases by .12 (or 12 percentage points)

If income goes up 1% then the probability of smoking decreases by .00012 (or .012 percentage points)

If income goes up 1% then the probability of smoking increases by .00012 (or .012 percentage points)

If income goes up 1% then the probability of smoking increases by 1.2 (or 12 percentage points)

Define Octane number and Cetane number?

in 200 words

The data below collected for the number of at bats and the number of hits in the world series:

1. 1. Draw a scatterplot (10 points)

2. 2. Find the correlation coefficient r (45 points)

3. 3. Find the equation of the regression line and graph the equation on the scatterplot (35 points)

4. 4. How many hits would a player get if the player had 60 at bats? (10 points)

In general, if p is the number of predictor variables and k is the number of groups for the outcome variable in a DA, how many different discriminant functions can be obtained to differentiate among
groups? (This question assumes that the X predictor variables have a determinant that is nonzero; that is, no individual Xi predictor variable can be perfectly predicted from scores on one or more other X
predictor variables.)

What is a random number? and what are the criteria for a random number? For a research need that requires random numbers, a random number generator is needed, how does this random number generator work?

In java:

A complex number is a number in the form a + bi, where a and b are real numbers and i is sqrt( -1). The numbers a and b are known as the real part and imaginary part of the complex number, respectively.

You can perform addition, subtraction, multiplication, and division for complex numbers using the following formulas:

a + bi + c + di = (a + c) + (b + d)i
a + bi - (c + di) = (a - c) + (b - d)i
(a + bi) * (c + di) = (ac - bd) + (bc + ad)i
(a+bi)/(c+di) = (ac+bd)/(c^2 +d^2) + (bc-ad)i/(c^2 +d^2)

You can also obtain the absolute value for a complex number using the following formula:

| a + bi | = sqrt(a^2 + b^2)

(A complex number can be interpreted as a point on a plane by identifying the (a, b) values as the coordinates of the point. The absolute value of the complex number corresponds to the distance of the point to the origin, as shown in Figure 13.10.)

Design a class named Complex for representing complex numbers and the methods add, subtract, multiply, divide, and abs for performing complex number operations, and override the toString method for returning a string representation for a complex number. The toString method returns (a + bi) as a string. If b is 0, it simply returns a. Your Complex class should also implement Cloneable and Comparable. Compare two complex numbers using their absolute values.

Provide three constructors Complex(a, b), Complex(a), and Complex(). Complex() creates a Complex object for number 0 and Complex(a) creates a Complex object with 0 for b. Also provide the getRealPart() and getImaginaryPart() methods for returning the real and imaginary part of the complex number, respectively.

Use the code at

https://liveexample.pearsoncmg.com/test/Exercise13_17.txt

to test your implementation.

Sample Run

Enter the first complex number: 3.5 5.5

Enter the second complex number: -3.5 1

(3.5 + 5.5i) + (-3.5 + 1.0i) = 0.0 + 6.5i

(3.5 + 5.5i) - (-3.5 + 1.0i) = 7.0 + 4.5i

(3.5 + 5.5i) * (-3.5 + 1.0i) = -17.75 -15.75i

(3.5 + 5.5i) / (-3.5 + 1.0i) = -0.5094339622641509 -1.7169811320754718i

|3.5 + 5.5i| = 6.519202405202649

false

3.5

5.5

[-3.5 + 1.0i, 4.0 + -0.5i, 3.5 + 5.5i, 3.5 + 5.5i]

Class Name: Exercise13_17

            Chromosome Chromosome

            Locus Number Locus   Number                     

Table 1.

1. If you haven’t already done so, calculate the RMP for each of Jane’s loci using the provided allelic frequency information in Table 1 above.  Please show your work.

2. What are the chances of two people sharing Jane’s TPOX and TH01 alleles?  Please show your work. (You may use exponents and round off your answer to two decimal places, eg: 1.21 x 10^-7)

3. What are the chances of someone sharing Jane’s TPOX and TH01 and FGA alleles?  Please show your work. (You may use exponents and round off your answer to two decimal places, eg: 1.21 x 10^-7)

4. Now calculate the total RMP (random match probability) that Jane’s DNA profile above matches the crime scene DNA purely by coincidence? Please show your work. (You may round off your answer to two decimal places and use exponents, eg: 1.21 x 10^-7)

Simulation Case Study:
Phoenix Boutique Hotel Group

Phoenix Boutique Hotel Group (PBHG) was founded in 2007 by Bree Bristowe. Having worked for several luxury resorts, Bristowe decided to pursue her dream of owning and operating a boutique hotel. Her hotel, which she called PHX, was located in an area that included several high-end resorts and business hotels. PHX filled a niche market for “modern travelers looking for excellent service and contemporary design without the frills.” Since opening PHX, Bristowe has invested, purchased, or renovated three other small hotels in the Phoenix metropolitan area: Canyon Inn PHX, PHX B&B, and The PHX Bungalows.

One of the customer service enhancements Bristowe has implemented is a centralized, toll-free reservation system. Although many customers book specific hotels online, the phone reservation system enables PBHG to find the best reservation match at all properties. It has been an excellent option for those customers who have preferences regarding the type of room, amenity options, and the best price across the four hotel locations.

Currently, three agents are on staff for the 6 a.m. to 2 p.m. call shift. The time between calls during this shift is represented in Table 1. The time to process reservation requests during this shift is in Table 2.

Table 1: Incoming Call Distribution

Table 2: Service Time Distribution

Bristowe wants to ensure customers are not on hold for longer than 2 minutes. She is debating hiring additional staff for this shift based on the available data. Additionally, Bristowe and PBHG will soon be featured in a national travel magazine with a circulation of over a million subscriptions. Bristowe is worried that the current operators may not be able to handle the increase in reservations. The projected increase for call distribution is represented in Table 3.

Table 3: Incoming Call Distribution

Bristowe has asked for your advice in evaluating the current phone reservation system. Create a simulation model to investigate her concerns. Make recommendations about the reservation agents.