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 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.

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.

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 ?(? | ?).

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=____?

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]

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.

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:

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 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)?

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?

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?

1. A new process has been developed for applying photoresist to 125-mm silicon wafers used in manufacturing integrated circuits. Ten wafers were tested, and the following photoresist thickness measurements (in angstroms x1000) were observed:
   13.3987, 13.3957, 13.3902, 13.4015, 13.4001, 13.3918, 13.3965, 13.3925, 13.3946, and 13.4002.
   (a) Test the hypothesis that mean thickness is 13.4 x 1000Å. Use = 0.05 and assume a two sided
   alternative.
   (b) Find a 99% two-sided confidence interval on mean photoresist thickness. Assume that thickness
   is normally distributed.
   (c) Does the normality assumption seem reasonable for these data?

Joan's Nursery specializes in custom-designed landscaping for residential areas. The estimated labor cost associated with a particular landscaping proposal is based on the number of plantings of trees, shrubs, and so on to be used for the project. For cost-estimating purposes, managers use two hours of labor time for the planting of a medium-sized tree. Actual times from a sample of 10 plantings during the past month follow (times in hours).

With a 0.05 level of significance, test to see whether the mean tree-planting time differs from two hours.

(a)State the null and alternative hypotheses.

a)H₀: μ ≤ 2

H_a: μ > 2

b)H₀: μ < 2

H_a: μ ≥ 2

c)H₀: μ = 2

H_a: μ ≠ 2

d)H₀: μ ≥ 2

H_a: μ < 2

e)H₀: μ > 2

H_a: μ ≤ 2

(b)Compute the sample mean.

(c)Compute the sample standard deviation. (Round your answer to three decimal places.)

(d)What is the test statistic? (Round your answer to three decimal places.)

test statistic=

What is the p-value? (Round your answer to four decimal places.)

p-value =

(e)What is your conclusion?

Do not reject H₀. We can conclude that the mean tree-planting time differs from two hours. There is a reason to change from the two hours for cost estimating purposes.

Reject H₀. We cannot conclude that the mean tree-planting time differs from two hours. There is no reason to change from the two hours for cost estimating purposes.    

Do not reject H₀. We cannot conclude that the mean tree-planting time differs from two hours. There is no reason to change from the two hours for cost estimating purposes.

Reject H₀. We can conclude that the mean tree-planting time differs from two hours. There is a reason to change from the two hours for cost estimating purposes.

Suppose you work for a survey research company. In a typical survey, you mail questionnaires to 150 companies. Of course, some of these companies might decide not to respond. Assume that the nonresponse rate is 45%; that is, each company's probability of not responding, independently of the others, is 0.45. Round your answers to three decimal places and if your answer is zero, enter "0". a. If your company requires at least 90 responses for a valid survey, find the probability that it will get this many. Use a data table to see how your answer varies as a function of the nonresponse rate (for a reasonable range of response rates surrounding 45%).

I cannot get a table to work with the probabilities for

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

I am asking the R studio Code, pleas leave your code and comment here, thanks a lot!

Q1.The data file abrasion contains the results from a small scale study (Davies, O.L. and Goldsmith, P.L. Statistical methods in Research and Production, 1972),  of the relation between rubber's resistance to abrasion (Y) and rubber hardness (X1) and rubber tensile strength (X2).

The data set abrasion is in Course Content -> Data Sets AL -> Ch04

• Import the data set into R.
• Obtain the scatter plot matrix and the correlation matrix.You can do this together using the commands in the file pairs.r

Upload the results here (one file in .png or .pdf formats) - Remember to include a title.

Q2.

Run the regression model. Obtain the estimates of the coefficients (round answer to 4 decimal places, it the answer is 7.5e-08 enter 0)

Which variable is significant? __ (enter exactly on of the three options: x1, x2 or both)

Q3.

Enter here the coefficient of determination (adjusted R-squared). Round your answer to 4 decimal places.

Q4.

Enter here the estimate for σ, that is s or the residual standard error. Round your answer to 2 decimal places.

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.