. Taxation and comparative statics with small changes:
a. Given that ??/?? represents the tax incidence on consumers in equation, (??/??= ?/(?−?))what is the expression for the tax incidence on firms in terms of η & ε. What does the sum of the tax incidence on consumers and firms equal? In no more than two sentences, explain why they must sum to this number.
b. Now consider another scenario, the imposition of a specific tax (?) that is paid directly to the
government by consumers rather than by firms as in part (a). Under such a tax, the equilibrium
condition is now: ?(?∗(?) + ?) = ?(?∗(?)). This condition sets a general demand function equal to a
general supply function, shows that the equilibrium price P* is an implicit function of ?, and makes
explicit that the amount now paid for the good by consumers with the tax is ?∗ + ?. Use this equilibrium
condition to find ??/??.
c. In part (a) P* represents the price consumers pay. What does P* represent in part (b)?
d. Should it be surprising that your answers to parts (a) and (b) represent the same tax incidence for firms?
Support your answer in no more than three sentences.
In: Math
Suppose that Y has the gamma distribution with parameters a ( shape ) = 2 and b (scale) = 2. Use R to plot the probability density, and determine the shape or skewness for the gamma distribution.
Use R code
a. )Skew to the left |
||
b.) |
Skew to the right |
|
c.) |
symmetrical |
|
d.) |
bell curved |
In: Math
Describe the steps necessary to calculate the variance of a sample. Why is it important to understand variance?
Discuss a situation in which you have used the variance of a sample to help solve a problem.
In: Math
According to a study done by a university student, the probability a randomly selected individual will not cover his or her mouth when sneezing is .267
Suppose you sit on a bench in a mall and observe people's habits as they sneeze.
(a) What is the probability that among 12 randomly observed individuals exactly 6 do not cover their mouth when sneezing?
(b) What is the probability that among 12 randomly observed individuals fewer than 3 do not cover their mouth when sneezing?
(c) Would you be surprised if, after observing 12 individuals, fewer than half covered their mouth when sneezing? Why?
In: Math
In their book Introduction to Linear Regression Analysis (3rd edition, Wiley, 2001) Montgomery, Peck, and Vining present measurements on NbOCl3 concentration from a tube-flow reactor experiment. The data, in gram-mole per liter × 10–3, are as follows. Construct a stem-and-leaf diagram for this data. Compute the sample mean, sample standard deviation, and the sample median.
450 | 450 | 562 | 429 | 434 | 463 | 437 | 1258 | 1220 |
1164 | 1052 | 977 | 1183 | 1273 | 1303 | 1496 | 1503 | 1692 |
1752 | 2752 | 3212 | 3212 | 3378 | 1909 | 2558 | 2650 | 2808 |
In: Math
Loss,x1,x2 372,45,162 206,55,233 175,61,232 154,66,231 136,71,231 112,71,237 55,81,224 45,86,219 221,53,203 166,60,189 164,64,210 113,68,210 82,79,196 32,81,180 228,56,200 196,68,173 128,75,188 97,83,161 64,88,119 249,59,161 219,71,151 186,80,165 155,82,151 114,89,128 341,51,161 340,59,146 283,65,148 267,74,144 215,81,134 148,86,127
Need the code and comment in R-studio, and please explain it, thanks!
Q5.
Use your model to obtain the mean abrasion loss for rubber with hardness 71 an tensile strength 201. Round your answer to 2 decimal places.
Q6.
Use your model to obtain a 98% confidence interval for the mean abrasion loss for rubber with hardness 71 an tensile strength 201.
Enter here the Lower Bound for the confidence interval. Round your answer to 2 decimal places.
Q7.
After the scatter plots, the correlation between the variables, the summary of the model, R-squared and s, and the F-test, briefly comment on the adequacy of the model fit.
In: Math
An 10-bit password is required to access a system. A hacker systematically works through all possible 10-bit patterns. Let ? be the number of patterns tested until the correct password is found.
(a) Find ?? and the pmf of ?.
Let ? be the event that the password has not been found after 24 tries.
(b) Find the conditional pmf of ? given ?.
(c) Find ?(?) and ?(? | ?).
In: Math
1) In order to find a 89% confidence interval we need to find values a and b such that for Z ~ N (mu=0, sigma=1), P(a<Z<b)=0.89.
(a) Suppose a= -2.8418. Then b=____?
(b) Suppose b=2.036. Then a=____?
In: Math
1.When students apply for graduate studies (i.e. at the master’s
or doctoral level), they are
required to submit an official copy of their transcript, mailed
directly from the Registrar’s
Office at their academic institution. The customer service division
of the Registrar’s
Office at a large Canadian university is interested in determining
if they are more than
25% faster at processing transcripts than another university in the
area, which can process
transcripts in 16 business hours. The customer service manager
obtains a random sample
of 10 waiting times (in business hours), which are provided
below.
11 12 18 20 23
15 10 12 13 14
a. Conduct an appropriate hypothesis test. Use the critical value
method. Use a
population standard deviation of 2 hours. [9 marks]
HINT: You will first have to determine what it means to be 25%
faster, in terms
of hours.
b. Explain what a Type I Error means in this context. [1 mark]
2. A major keyboard manufacturer has a line of keyboards designed
for apartment dwellers.
These keyboards need to be light enough to be carried up flights of
stairs. The lead
engineer wants to use a new type of material. The engineer claims
that the new keyboards
will be lighter than the old keyboards.
They take a sample of 4 keyboards manufactured using the old
material and compute an
average weight of 21 kg with a standard deviation of 1 kg.
They take a sample of 8 keyboards manufactured using the new
material and compute an
average weight of 17 kg with a standard deviation of 2 kg.
a. Conduct an appropriate hypothesis test using the p-value method.
Use the old
material as population 1. [8 marks]
b. How much evidence is there against the null hypothesis in part
(a)? [1 mark]
c. Explain what a Type II Error means in this context. [1 mark
3.An insurance company is interested in estimating the
population mean cost of basic dental
cleaning at dentists in Saskatoon. Suppose there are only two
dentists in Saskatoon:
Dentist A and Dentist B. Suppose also that the cost of basic dental
cleaning varies only
depending on how well the patient practices regular dental hygiene,
so that the cost of
basic dental cleaning roughly follows a Normal distribution
regardless of the dentist.
The insurance company selects 8 sample patients and sends them to
both Dentist A and
Dentist B. They send the patients in random order, such that half
of the patients are seen
by Dentist A first, and half are seen by Dentist B first, so as not
to bias the results. The
cost of basic dental cleaning for these 8 patients seen by both
Dentists A and B are
provided below. The insurance company would like to determine
whether the population
mean cost of basic dental cleaning by Dentist A is different from
the population mean
cost of basic dental care by Dentist B. Let the population of costs
of basic dental care
from Dentist A be population 1.
Patient 1 2 3 4 5 6 7 8
Dentist A $100 $120 $125 $110 $95 $105 $120 $115
Dentist B $150 $100 $140 $100 $95 $105 $100 $120
Conduct an appropriate hypothesis test using the critical value
method. [10 marks]
In: Math
The following appeared in the Wall Street Journal, September 16, 2019 "Letters to the Editor" that refers to a September 11 article that appeared in the Journal. Read the letter reproduced below in part and answer the question following the letter. "Phil Gramm and Mike Solon start “Warren’s Assault on Retiree Wealth” (op-ed, Sept. 11) by telling the reader that the households of ages 65 to 74 have an average of $1,066,000 in net worth. This may be technically true but it has little significance in a political or public-policy context. The (much more meaningful) median figure for the same age group is $224,000—less than one quarter of the figure they cite....." Tim McGlinn Maplewood, N.J. Which of the two measures of net worth, $1,066,000 from the original article, or the letter writers measure, $224,000, do you think is the superior measure to use? Explain fully and specifically.
In: Math
A professor has recently taught two sections of the same course with only one difference between the sections. In one section, he used only examples taken from sports applications, and in the other section, he used examples taken from a variety of application areas. The sports themed section was advertised as such; so students knew which type of section they were enrolling in. The professor has asked you to compare student performance in the two sections using course grades and total points earned in the course. You will need to import the Scores.csv dataset that has been provided for you:
Count | Score | Section |
10 | 200 | Sports |
10 | 205 | Sports |
20 | 235 | Sports |
10 | 240 | Sports |
10 | 250 | Sports |
10 | 265 | Regular |
10 | 275 | Regular |
30 | 285 | Sports |
10 | 295 | Regular |
10 | 300 | Regular |
20 | 300 | Sports |
10 | 305 | Sports |
10 | 305 | Regular |
10 | 310 | Regular |
10 | 310 | Sports |
20 | 320 | Regular |
10 | 305 | Regular |
10 | 315 | Sports |
20 | 320 | Regular |
10 | 325 | Regular |
10 | 325 | Sports |
20 | 330 | Regular |
10 | 330 | Sports |
30 | 335 | Sports |
10 | 335 | Regular |
20 | 340 | Regular |
10 | 340 | Sports |
30 | 350 | Regular |
20 | 360 | Regular |
10 | 360 | Sports |
20 | 365 | Regular |
20 | 365 | Sports |
10 | 370 | Sports |
10 | 370 | Regular |
20 | 375 | Regular |
10 | 375 | Sports |
20 | 380 | Regular |
10 | 395 | Sports |
Use the appropriate R functions to answer the following questions:
1. What are the observational units in this study?
2. Identify the variables mentioned in the narrative paragraph and determine which are categorical and quantitative?
3. Create one variable to hold a subset of your data set that contains only the Regular Section and one variable for the Sports Section.
4. Use the Plot function to plot each Sections scores and the number of students achieving that score. Use additional Plot Arguments to label the graph and give each axis an appropriate label. Once you have produced your Plots answer the following questions:
a. Comparing and contrasting the point distributions between the two section, looking at both tendency and consistency: Can you say that one section tended to score more points than the other? Justify and explain your answer.
b. Did every student in one section score more points than every student in the other section? If not, explain what a statistical tendency means in this context.
c. What could be one additional variable that was not mentioned in the narrative that could be influencing the point distributions between the two sections?
In: Math
In the EAI sampling problem, the population mean is $51,200 and the population standard deviation is $5,000. When the sample size is n=30, there is a 0.4908 probability of obtaining a sample mean within plus or minus $600 of the population mean. Use z-table.
a. What is the probability that the sample mean is within $600 of the population mean if a sample of size 60 is used (to 4 decimals)?
b. What is the probability that the sample mean is within $600 of the population mean if a sample of size 120 is used (to 4 decimals)?
In: Math
NSA electronics is experimenting with the manufacture of a new type of transistor that is very difficult to mass produce at an acceptable quality level. Every hour a supervisor takes a random sample of 8 transistors produced on the assembly line. From the past records, 15 per cent of transistors fail in quality inspection.
4a) NSA wants to know the probability of 0 to 8 defectives if the percentage of defective is 15%
4b) At 95% confidence level how many samples will be defective?
4c) At 99% confidence level how many samples will be defective?
In: Math
A meat-processing company in Alberta produces and markets a package of eight small sausage sandwiches. The product is nationally distributed, and the company is interested in knowing the average retail price charged across the country. A random sample of 25 retailers was selected giving a sample average retail price of $2.13. The population standard deviation is known to be $0.20.
A. What do you need to assume in order to compute a confidence interval for the interval for the population mean retail price charged across the country.
B. Compute a 99% confidence interval for the population mean retail price. Interpret your answer in terms of the question.
C. Suppose you wish to estimate the population mean retail price to within $0.05 with 99% confidence interval. Retailers should be sampled in order to achieve the desired margin of error?
In: Math
In: Math