For a sample of 12 trees, the volume of lumber (in m³) and the diameter ( in cm ) at a fixed height above the ground level was measured. The results were as follows.

Use Excel sheet

a)Construct a scatterplot of volume ( y ) versus diameter ( x ). using Excel

b)Compute the least-square line for predicting volume from diameter.

c)Compute the fitted value and residual for each point. d)If two trees differ in diameter by 8 cm, by how much would you predict their volume to differ?

e)Predict the volume of a tree whose diameter is 44 cm.

f)For what diameter would you predict a volume of 1m³

     I-Multiplication Rules

1. How many different slats can be made. If the splint is composed of 4 letters and 3 digits.

2. How many special shuttle crews can be formed if: for pilot position, co-pilot and flight engineer there are (8) eight candidates, for two scientists one for solar experiment and one for stellar experiment there are (6) candidates and for two Civilians there are (9) candidates.

II-permutations and combinations

1. In a raffle where there are 10 possible numbers in each ball, if three pellets are extracted. How many ways is it possible to combine extracted numbers?

2. Ten people reach a row at the same time. How many ways can they be formed?

3. In a Olympiad there are 10 swimmers in a race, how many ways can arrive the first three places?

4. How many committees of three teachers can be made if there are 6 teachers to choose from?

One football player was tired of teachers and students making comments under the general assumption that student-athletes were less intelligent or inferior students to those not playing sports. To get rid of the “dumb jock” labels, he compared the results on a college readiness assessment of student-athletes and non-athletes. On this particular assessment, a student could receive the following scores: “under-prepared,” “on-track,” or “college-ready.” He recorded the following chart:

An experiment is planned to compare three methods of instruction. Each is tested with a single classroom of 25 students. A different instructor is to be used for each classroom and consequently each instruction method. a. Write a short critique of the proposed experiment. b. How could the experiment be improved?

Conduct a test at the alphaαequals=0.01 level of significance by determining ​(a) the null and alternative​ hypotheses, ​(b) the test​ statistic, and​ (c) the​ P-value. Assume the samples were obtained independently from a large population using simple random sampling.Test whether

p 1 greater than p 2p1>p2. The sample data are x1=118​, n1=259​, x2=141​, and n2=313.

​(a) Choose the correct null and alternative hypotheses below.

A.

Upper H 0 : p 1 equals p 2H0: p1=p2

versus Upper H 1 : p 1 greater than p 2H1: p1>p2

B.

Upper H 0 : p 1 equals p 2H0: p1=p2

versus Upper H 1 : p 1 not equals p 2H1: p1≠p2

C.

Upper H 0 : p 1 equals p 2H0: p1=p2

versus Upper H 1 : p 1 less than p 2H1: p1<p2

D.

Upper H 0 : p 1 equals 0H0: p1=0

versus Upper H 1 : p 1 not equals 0

B) Test the statistics

C) Find the P-value

Find out the 95% confidence interval for a sample whose Mean=10.50 and Standard Deviation is= 2.0. The sample size is n=50.

** please I need the answer in the computer typing not hand writing.

Subject: Statistic

1. (4 pts)The playing life of a sunshine radio is normally distributed with a mean of 500 hours and a standard deviation of 60 hours.

1. What percent of the radios will last from 500 to 620 hours?

2. What percent of radios will last less than 500 hours?

3. What percent of radios will play between 560 and 620 hours?

Control chart systems can operate on two basic methods of measurement. State these two methods and briefly distinguish between them, giving three examples of industrial processes where each might be applied. Specify an appropriate sampling procedure in each case.

What is the most noticeable findings and observations of this data set? What sticks out?

Please put these in order- highest to lowest- and tell me HOW you did it. SHOW me please your answer and in excel or google sheets

A research project has been tracking the health and cognitive functions of the elderly population in Arizona. The table below shows the memory test scores from 16 elderly residents, tested first when they were 65 years old and again when they were 75 years old. The researcher wants to know if there is a significant decline in memory functions from age 65 to age 75 based on this sample. In other words, it is hypothesized that the memory score at age 75 is significantly lower than the memory score at age 65. So the null and alternative hypotheses should be directional. The alpha level was set at α = .05 for a one-tailed hypothesis test.

a. Identify the dependent variable (this is the outcome measure) and the independent variable (this is what differentiates the two groups of data points being compared). (1 point total: .5 for DV, .5 for IV)

b. Explain why a paired-samples t test is appropriate for answering this research question. (1 point)

c. What would be the null and alternative hypotheses in both words and symbol notations? (2 points total: 1 for each hypothesis, .5 for written and .5 for notation)

d. Calculate the difference score by subtracting each “Age 65” score from the associated “Age 75” score for each subject. Fill in the column in the table below for “difference score.” (1 point total: deduct .5 for each error up to 1 point.)

Hint: The difference score is calculated as (age 75 minus age 65), so a negative number indicates a decline in memory performance, which is the researcher’s hypothesis.

e. Calculate the mean from the sample of difference scores (1 point total: .5 if process is correct but answer is wrong)

f. Estimate the standard deviation of the population of difference scores (1 point total: .5 if process is correct but answer is wrong)

g. Calculate the standard error (standard deviation of the sampling distribution) (1 point total: .5 if process is correct but answer is wrong)

h. Calculate the t statistic for the sample of difference scores (1 point total: .5 if process is correct but answer is wrong)

i. Figure out the degree of freedom, and then determine the critical t value(s) based on the type of test and the preset alpha level. (1 point total: .5 for df, .5 for critical t value)

j. Compare the t statistic with the critical t value. Is the calculated t statistic more extreme or less extreme than the critical t value? Then make a decision about the hypothesis test, stating explicitly “reject” or “fail to reject” accordingly. (2 points total: 1 for each answer)

k. Interpret the result in 1-2 sentences to answer the research question (you may use the wording from the hypothesis or explain it in your own words) (1 point)

l. Calculate the standardized effect size of this hypothesis test (1 point: .5 if process is correct but answer is wrong)

Write a program to choose a random number X in the interval [2,10] 1000 times and record what fraction of the outcomes satisfy X > 5, what fraction satisfy 5 < X < 7, and what fraction satisfy x2 −12x+35 > 0. How do these results compare with Exercise 1?

I want this to be solved using R studio or R software, please.

Here is the example:

The data in stat4_prob5 present the performance of a chemical process as a function of sever controllable process variables.

1. (a) Fit a multiple regression modelrelating CO2product (y) to total solvent (x1) and hydrogen consumption (x2) and report the fitted regression line.
2. (b) Find a point estimatefor the variance term σ2.
3. (c) Construct the ANOVA tableand test for the significance of the regression using

α = 0.05.

4. (d) Using individual t-tests determine the contribution of x1 and x2 to the model using α = 0.05.

Here is the data:

y=c(36.98, 13.74, 10.08, 8.53, 36.42, 26.59, 19.07, 5.96, 15.52, 56.61, 26.72, 20.80, 6.99, 45.93, 43.09, 15.79, 21.60, 35.19, 26.14, 8.60, 11.63, 9.59, 4.42, 38.89, 11.19, 75.62, 36.03)

x1=c(2227.25, 434.90, 481.19, 247.14, 1645.89, 907.59, 608.05, 380.55, 213.40, 2043.36, 761.48, 566.40, 237.08, 1961.49, 1023.89, 411.30, 2244.77, 978.64, 687.62, 468.28, 460.62, 290.42, 233.95, 2088.12, 994.63, 2196.17, 1080.11)

x2=c(2.06, 1.33, 0.97, 0.62, 0.22, 0.76, 1.71, 3.93, 1.97, 5.08, 0.60, 0.90, 0.63, 2.04, 1.57, 2.38, 0.32, 0.44, 8.82, 0.02, 1.72, 1.88, 1.43, 1.35, 1.61, 4.78, 5.88)

In a cognitive psychology experiment, the researcher is interested in whether encoding condition has an effect on memory for a list of words. She recruits 16 subjects to participate in the experiment. Each subject comes to the lab twice to be tested in two different encoding conditions and their memory performance scores are listed below. The researcher would like to leave the hypothesis non-directional without predicting which encoding condition would lead to better memory, and she sets the significance level at α = .05 for a two-tailed test.

a. Identify the dependent variable (this is the outcome measure) and the independent variable (this is what differentiates the two groups of data points being compared). (1 point total: .5 for DV, .5 for IV)

b. What would be the null and alternative hypotheses in both words and symbol notations? (2 points total: 1 for each hypothesis, .5 for written and .5 for notation)

Perform the steps below to get the t statistic for the sample:

c. Calculate the difference scores and enter them into the table below. (1 point, deduct .5 for each error up to 1 point total)

d. Mean of sample (1 point: .5 if process is correct but answer is wrong)

e. Estimated population standard deviation (1 point: .5 if process is correct but answer is wrong)

f. Standard error (1 point: .5 if process is correct but answer is wrong)

g. Calculated t statistic (1 point: .5 if process is correct but answer is wrong)

With the calculated t statistic, perform the following steps to conclude the hypothesis test.

h. Critical t value (1 point: .5 if process is correct but answer is wrong)

i. Compare the t statistic with the critical t value. Is the calculated t statistic more extreme or less extreme than the critical t value? Then make a decision about the hypothesis test, stating explicitly “reject” or “fail to reject” accordingly. (1 points total: .5 for each answer)

j. Interpret the result in 1-2 sentences to answer the research question (you may use the wording from the hypothesis or explain it in your own words) (1 point)

k. Calculate the standardized effect size of this hypothesis test (1 point: .5 if process is correct but answer is wrong)

If you pay more in tuition to go to a top business​ school, will it necessarily result in a higher probability of a job offer at​ graduation? Let y=percentage of graduates with job offers and x=tuition ​cost; then fit the simple linear​model, E(y)=β0+β1x​,

to the data below. Is there sufficient evidence​ (α=0.10 of a positive linear relationship between y and​ x?

Give the null and alternative hypotheses for testing whether there exists a positive linear relationship between y and​ x?

A.H0​: β1s=0

Ha​:β1<0

B. H0​: β0=0

Ha​:β<0

C.H0​: β0=0

Ha​:β0>0

D. HO:β0:=0

Ha​: β0≠0

E. H0​: β1=0

Ha​: β1>0

F. H0​:β1=0

Ha​:β1≠0 .

Find the test statistic.

t=___________ ​(Round to two decimal places as​ needed.)

Find the​ p-value.​p-=______________ ​(Round to four decimal places as​ needed.)

Make the appropriate conclusion = ALPHA=0.10

Choose the correct answer below.

A.

Do not reject

H0. There is

insufficient

evidence that there exists a positive linear relationship between y and x.

B.

Do not reject

H0.

There is

sufficient

evidence that there exists a positive linear relationship between y and x.

C.

Reject

H0.

There is

insufficienti

evidence that there exists a positive linear relationship between y and x.

D.

Reject

H0.

There is

sufficient

evidence that there exists a positive linear relationship between y and x.

Click to select your answer(s).