Question 1: William Comanor and Thomas Wilson1 specified the following regression in their study of advertising’s effect on the profit rates of 41 consumer goods firms: PRi = β0 + β1 ×ADVi/SALESi + β2 ×lnCAPi + β3 ×lnESi + β4 ×lnDGi + i where: PRi = the profit margin of the ith firm ADVi = the advertising expenditures in the ith firm (in dollars) SALESi = the total gross sales of the ith firm (in dollars) CAPi = the capital needed to enter the ith firm’s market at an efficient size ESi = the degree to which economies of scale exist in the ith firm’s industry DGi = percent growth in sales (demand) of the ith firm over the last 10 years a) Hypothesize expected signs for each of the slope coefficients. b) Note that there are two different kinds of nonlinear (in the variables) relationships in this equation. For each independent variable, determine the shape that the chosen functional form implies, and state whether you agree or disagree with this shape. Explain your reasoning in each case. c) Comanor and Wilson state that the simple correlation coefficient between ADVi/SALESi and each of the other independent variables is positive. If one of these other variables were omitted, in which direction would ˆ β1 likely be biased? Refer to your hypothesized signs of the coefficients in part (a).

data information

NAME:  Hat measurements, including hat size
TYPE:  Observational
SIZE:  26 observations, 6 variables

DESCRIPTIVE ABSTRACT:
 
The dataset contains hat size as well as circumference, length of major axis 
and length of minor axis of the inner hat band for 26 hats. The manufacturer 
and the country of manufacture are also included.

SOURCE:

Katherine Brady and Kari Cornelius, Carleton College ('96) students, gathered 
the observations from hats at a store at the Mall of America in Bloomington, 
Minnesota.

VARIABLE DESCRIPTIONS:

Variables 
1         Hat size
2         Circumference (inches)
3         Length of major axis (inches)
4         Length of minor axis (inches)
5         Where made? Italy = 1, U.S.A. = 2
6         Manufacturer? Beaver = 1, Borsalino = 2, Dobbs = 3, Stetson = 4

please answer the follow question

How many variables are there, and how are they defifined?

• Which variables are quantitative and which are categorical?

• What are the units of measurement for each quantitative variable?

• What questions do you plan to investigate in your project? These may be questions that were of interest

to the researchers who collected data, or they may be questions that you thought of yourself. Make sure to

include questions that you can hope to answer using methods from this course.

One of the consequences of the economic meltdown in Great Recession has been a free fall of the stock market's average price/earning ratio, or P/E ratio. Generally, a high P/E ratio suggest that investors are expecting higher earnings growth in the future compared to companies with a lower P/E ratio. A Wall Street analyst wants to determine if the P/E ratio of rms in the footwear industry is dierent from the overall average of 20. The table below shows that P/E ratio for a sample of six rms in the footwear industry: Firm P/E ratio Collective Brands, Inc. 9.33 Cros,Inc. 22.63 DSW, Inc. 14.42 Nike, Inc. 18.68 Sketchers USA, Inc 9.35 Timberland Co. 14.93 a. (3 points) Let µ be the overall average P/E ratio. State the null and the alternative hypothesis in order to test whether the P/E ratio of rms in the footwear industry diers from the overall average of 20. b. (3 points) What is the average P/E ratio among the six footwear rms, i.e., x¯ =? c. (3 points) What is the standard deviation of the P/E ratio among the six footwear rms, i.e., s =? (Please around your answer to 4 decimal places. d. (3 points) Construct a 90% condence interval of the overall average P/E ratio, i.e., 90% condence interval of µ. (Please around your answer to 4 decimal places.) e. (2 point) Calculate the value of test statistic. (Please around your answer to 3 decimal places.) f. (4 points) Approximate the p-value in this test? g. (3 points) Does the P/E ratio of rms in the footwear industry dier from the overall average of 20? Please explain.

For the t test , one uses ----------------instead of σ

a. n

b. s

c. χ²

d. t

Using the Z table, find the critical value for

a) α  = .05, two-tailed test

b) α = .01, two tailed test

c) α = .10, two-tailed test

only 2 questions

((PLSS with steps and clear hand written PLSSS and thank you sooooo much for helping me))

As part of a long-term study of individuals 65 years of age or older, sociologists and physicians at the Wentworth Medical Center in upstate New York investigated the relationship between geographic location, gender and depression. A sample of 60 individuals, all in reasonably good health, was selected; 20 individuals were residents of Florida, 20 were residents of New York, and 20 were residents of North Carolina. Each of the individuals sampled was given a standardized test to measure depression. The data collected follow; higher test scores indicate higher levels of depression.

........

l) Is the depression in gender affect by the Geographic locations? Use a 0.05 level of significance.

m)

locations (Florida) (New York) North Carolina

Number of depressed (23for Florida ) (17for NY) (20for North C)persons

Is the distribution of the depressed peoples across locations uniform

(?FL = 33%, ?NY = 33%, ? NC= 33% )? Use a 0.05 level of significance.

In a test of the effectiveness of garlic for lowering​ cholesterol, 44 subjects were treated with garlic in a processed tablet form. Cholesterol levels were measured before and after the treatment. The changes ​(before−​after) in their levels of LDL cholesterol​ (in mg/dL) have a mean of 3.2 and a standard deviation of 17.2. Construct a 95​% confidence interval estimate of the mean net change in LDL cholesterol after the garlic treatment. What does the confidence interval suggest about the effectiveness of garlic in reducing LDL​ cholesterol?  

_____ mg/dL < population mean < ______ mg/dL

Your scores from an afternoon of bowling were 128, 189, 156, 143, 117, and 152. Your sisters bowling scores were 204, 176, 189, 198, 218, 177, 190,and 203. Find the(two-sided) 98% confidence interval for (sigma^2*you) /(sigma^2*Sister). Assume bowling is normally distributed.

Marv Johnson, city manager of Filkburg, Virginia, wants to develop a better understanding of the factors that influence vehicles maintenance and costs. Mr. Johnson has data on 100 vehicles in the city’s vehicle fleet. The dependent variable is the annual maintenance cost per vehicle (MCOST). The independent variables include total vehicle mileage (TMILE), a dummy variable coded1 for emergency service vehicles and coded 0 for all other types of vehicles (VTYPE). Assist Mr. Johnson by generating a regression equation using these data. What substantive conclusions can be reached about factors that affect vehicle maintenance costs?

A randomized controlled study was done (Lewis et al, Annals of Internal Medicine, 1998) to see whether the cholesterol lowering drug pravastatin can lower the risk of coronary disease in older patients after myocardial infarction.

Results

Major coronary events occurred in 28.1% of placebo recipients and 19.7% of pravastatin recipients (difference, 9.0 percentage points [95% CI, 4 to 13 percentage points]; relative risk reduction, 32%; P < 0.001). Coronary death occurred in 10.3% of the placebo group and in 5.8% of the pravastatin group (difference, 4.6 percentage points [CI, 1.9 to 6.5 percentage points]; relative risk reduction, 45%; P = 0.004). Stroke incidence was 7.3% in the placebo group and 4.5% in the pravastatin group (absolute reduction, 2.9 percentage points [CI, 0.3 to 4.5 percentage points]; relative reduction, 40%; P = 0.03).

All of the following statements regarding interpreting the numbers are true EXCEPT one. Which statement is NOT accurate?:

a. If we repeated the study on a similar sample of subjects, we would observe a difference of 9 percentage points or greater between pravastatin and placebo less than 1 in 1000 times if there were actually no difference between the groups.

b. We are 95% confident that the true reduction in coronary events from pravastatin compared with placebo is is between 4 and 13 percentage points.

c. Subjects receiving pravastatin had 55% of the risk of coronary death as the placebo group.

d. We are more than 95% confident that pravastatin reduces the risk of coronary events, coronary death, and stroke.

e. We are 97% confident that pravastatin reduced the risk of stroke by 2.9 percentage points compared with placebo.

7. In an American Animal Hospital Association survey, 37% of respondents stated that they talked to their pets on the telephone. A veterinarian found this result hard to believe, so he randomly selected 150 pet owners and discovered that 54 of them spoke to their pet on the telephone. At 0.05 significant level, test the result stated by the American Animal Hospital Association.

8. With a random sample 1026 adult Americans, 534 stated the amount of federal tax they have to pay is too high. Use 0.01 significant level to test the claim that at least half of Americans say federal tax is too high.

You are a primary researcher. Select a topic of interest. Form a research question that you will ask 25 people. The question should generate a range of quantitative data. Some examples are: “ On average, how many minutes a day do you spend texting?” or “ How many inches tall are you?” Note: Research question should start with “How often...” or, “On average, how many...” Do not ask a question like, “Do you like chocolate?” because responses are “yes” or “no . ” You need numbers. Note: Be specific. Do not ask “How many bottles of water do you drink?” Instead ask, “On average, how many 8 -oz. glasses of water do you drink in a day?” You need to collect numerical data. Your question should be clear, concise and unbiased. Part of your Discussion Board posting this week will be your research question. Your research question must be approved by instructor. Required: 1. List your raw data results in a column in Excel. 2. Construct a relative frequency distribution of your data. Remember each class should have the same width, for example class es of 0 to 5, 6 to 10, 11 to 15 etc. 3. Using Excel, calculate the mean and standard deviation of your distribution and interpret their meanings. 4. Calculate a 95 percent confidence interval for the mean of your distribution using the t-distribution and your sample standard deviation. 5. Comment on your results – what have you observed? This is important so think and write carefully Format: Use Excel Worksheets and text dialog boxes where appropriate with size 12 font.

1. Wayne’s favourite donut at Tim Hortons is the sour cream glazed donut. Tim Hortons claims that each of these donuts contains 320 calories. Suppose that the actual number of calories in a sour cream glazed donut varies according to a normal distribution with a mean of 317 calories and a standard deviation of 22 calories. Let X represent the number of calories in a randomly selected sour cream glazed donut from Tim Hortons.

(a) What is the probability that the next sour cream glazed donut Wayne consumes will contain at least 300 calories?

(b) What proportion of all sour cream glazed donuts contain between 310 and 330 calories?

(c) Tim Hortons can guarantee that only 1.5% of all sour cream glazed donuts contain more than how many calories?

Are there gender differences in the time spent using on social media? A time-tracking software was used to determine the average time on social media websites in a random sample of 31 men and 31 women. Men, on average, spent 49 minutes per day on social media websites, with the standard deviation of 25. Women, on average, spent 52 minutes per day on social media websites, with a standard deviation of 18. Use α=0.05.