Given the following times (in seconds) to process hot-rolled steel are observed for a random sample of size 12 as follows:

a/ Explain the difference between accuracy and precision of measurements.

b/ Explain the differences between the mean, median, and mode of the processing times.

c/ Compute the range, variance, and standard deviation of the processing times, and interpret them.

Cloud seeding has been studied for many decades as a weather modification procedure (for an interesting study of this subject, see the article in Technometrics, “A Bayesian Analysis of a Multiplicative Treatment Effect in Weather Modification,” Vol. 17, pp. 161–166). The rainfall in acre-feet from 18 clouds that were selected at random and seeded with silver nitrate follows: 18.0, 30.7, 19.8, 27.1, 22.3, 18.8, 31.8, 23.4, 21.2, 27.9, 31.9, 27.1, 25.0, 24.7, 26.9, 21.8, 29.2, and 34.8.

(a) Can you support a claim that mean rainfall from seeded clouds exceeds 25 acre-feet? Use α =0.01. Find the P-value.

(b) Check that rainfall is normally distributed.

(c) Compute the power of the test if the true mean rainfall is 27 acre-feet.

(d) What sample size would be required to detect a true mean rainfall of 27.5 acre-feet if you wanted the power of the test to be at least 0.9?

(e) Explain how the question in part (a) could be answered by constructing a one-sided confidence bound on the mean rainfall rate.

As personnel director, you want to test the perception of fairness of two methods of performance evaluation. 63 of 78 employees rated Method 1 as fair. 49 of 82 rated Method 2 as fair. At the .01 level, is there a difference in perceptions?

plz solve step by step

An engineer who is studying the tensile strength of a steel alloy intended for use in golf club shafts knows that tensile strength is approximately normally distributed withσ = 70 psi. A random sample of 12 specimens has a mean ten-sile strength of x = 3450 psi.

(a) Test the hypothesis that mean strength is 3500 psi. Use α = 0.05.

(b) What is the smallest level of significance at which you would be willing to reject the null hypothesis?

(c) What is the β-error for the test in part (a) if the true mean is 3470?

(d) Suppose that you wanted to reject the null hypothesis with probability at least 0.8 if mean strength μ = 3470. What sample size should be used?

(e) Explain how you could answer the question in part (a) with a two-sided confidence interval on mean tensile strength.

A) You want to estimate what percent of a school has a dog so you survey 50 people. 20 tell you they have a dog at home. What is your best guess at the true proportion of people who have a dog at home? What is your 95% confidence interval? Your 90% confidence interval? How many people would you need to survey to have a 95% confidence interval of 5% in length.

B) You ask the 20 people with dogs how much their dog weighs. You get a mean response of 30lbs with a standard deviation of 8lbs. What is your 95% confidence interval for the average weight of the school student's dog?

A government entity sets a Food Defect Action Level​ (FDAL) for the various foreign substances that inevitably end up in the foods we eat. The FDAL level for insect filth in peanut butter is 0.9 insect fragment​ (larvae, eggs, body​ parts, and so​ on) per gram. Suppose that a supply of peanut butter contains 0.9 insect fragment per gram. Compute the probability that the number of insect fragments in a 9​-gram sample of peanut butter is

​(a) exactly six. Interpret the results.

​(b) fewer than six. Interpret the results. ​

(c) at least six. Interpret the results.

​(d) at least one. Interpret the results.

​(e) Would it be unusual for a 9​-gram sample of this supply of peanut butter to contain eight or more insect​ fragments?

1.    You would like to estimate the starting salaries of recently graduated business majors (B.S. in any business degree). You randomly select 60 recently graduated business majors and get a sample mean of $43,800 and the population standard deviation is known to be $8,198

A.    Construct a 90% confidence interval to estimate the average starting salary of a recently graduated business major (Round to the nearest penny and state the answer as an interval – for example $351.89 to $728.14).

B.    Using the same confidence level, you would like the margin of error to be within $500, how many recently graduated business majors should you sample?

2.    You would like to estimate the amount of student loan debt a graduating senior will have at the time of repayment which begins in November. You randomly select 72 graduating seniors and get a sample mean of $31,172 with a standard deviation of $6,423. Construct a 98% confidence interval for the amount of debt a graduating senior will have. (Make sure you are careful selecting the correct values and that you round to the nearest penny. You will not get any credit if you are off by more than 1 cent.) (Round to the nearest penny and state the answer as an interval – for example $351.89 to $728.14).

3.    You would like to estimate the proportion of student loan debts that are in default. You randomly select 211 people who have student loans and find that 25 are in default.

A.    Construct a 95% confidence interval to estimate the proportion of student loans that are in default. (Round your sample proportion to 4 decimal points as well as round your margin of error to 4 decimal points. For example: .23916 would be .2392 and this represents 23.92%. State the answer as an interval – for example 27.36% to 31.43%).

B.    Using the same confidence level, you would like the margin of error to be with 3%, how many people with student loans should you sample?

Suppose there are three balls in a bag. One ball is black and two others are white. Three people, A, B and C, will pick a ball in this order. Instead of deciding the winner by the first black ball, the person who picks the black ball for the second time will be the winner. For example, if A picks the black ball for his first pick, A is not the winner. He just returns it to the bag. And then if B picks the black ball, B will be the winner because that is the second time the black ball is picked. A will start this game again, followed by B and C in this order. Obtain the formulas for the probability of winning for each person A, B, and C and then get their numerical estimates.

In 1,250-1,500 words, answer the following questions about possible research options.

1. Create a research question in the field of psychology that you are interested in researching. Write questions clearly. Include a brief background of the problem you are proposing and why it is important to the field of psychology.
2. State the null and alternative hypothesis (in both words and statistical notation) need to address the research question.
3. Choose which statistical test would be used to conduct the study and support it with research.
4. Describe the type of data needs to be collected to conduct the study and what techniques are best for collecting data.

Can you give me an example of one please?

This problem involves using R to examine the Central Limit Theorem more in detail. For all answers in this problem, round to four decimal places.

We will first generate 10 Poisson(λ=1) random variables and then calculate the sample mean of these 10 random variables. We will do this process 10,000 times to generate 10,000 simulated sample means. Run the following code and use the output to answer the following questions.

set.seed(2020)

nsims = 10000 # number of simulations
means = rep(0,nsims) # vector to store sample mean from each simulation

for(i in 1:nsims){
data = rpois(n=10,lambda=1)
means[i] = mean(data)
}

hist(means)
mean(means)
sd(means)


(d) From theory, what is SE[X] for this example? (This is a hand calculation not using R.)

(e) What proportion of the simulated sample means are less than 0.9? (If you don't remember how to do this operation in R, look back at your previous homework assignments.)

(f) Using the Central Limit Theorem, calculate the (approximate) probability that P(X < 0.9) for n=10 and λ=1. (This is a hand calculation not using R.)


Now, we want to explore how sample size has an impact on the distribution of the sample mean. Using the code above, adjust the sample size to run simulations for n=1, n=5, and n=100.



(i) Suppose we want a theoretical standard error of 0.25. What should be our sample size? (This is a hand calculation not using R.)

(j) Using the provided code above and the sample size you found in (i) and use R to complete 10,000 simulations. What is the standard deviation of the simulated sample means?

(k) Which of the following are true? (Check all that apply)

Even if our data is not normally distributed, the distribution of sample means will be approximately normally distributed for a sufficiently large sample size.

The sample mean converges to the population mean, as the sample size increases.

As the sample size increases, the standard errors tend to increase.

The Central Limit Theorem only applies to data that is normally distributed to begin with.

The ANES data below is on age and an ownership index (house + savings + stocks/bonds) for the group classified as “conspiracy theorists.” Is there a relationship between these two variables? By hand or using Excel (Excel is recommended) create a regression equation, calculate r and r² and interpret the results. Then calculate predicted ownership scores for a 25 year old person and an 80 year old person. Show as much work as possible.

Case    Age     Ownership Score

A         42        2

B         62        3

C         62        1

D         67        1

E          37        0

F          47        0

A television station wishes to study the relationship between viewership of its 11 p.m. news program and viewer age (18 years or less, 19 to 35, 36 to 54, 55 or older). A sample of 250 television viewers in each age group is randomly selected, and the number who watch the station’s 11 p.m. news is found for each sample. The results are given in the table below.

(a) Let p₁, p₂, p₃, and p₄ be the proportions of all viewers in each age group who watch the station’s 11 p.m. news. If these proportions are equal, then whether a viewer watches the station’s 11 p.m. news is independent of the viewer’s age group. Therefore, we can test the null hypothesis H₀ that p₁, p₂, p₃, and p₄ are equal by carrying out a chi-square test for independence. Perform this test by setting α = .05. (Round your answer to 3 decimal places.)

χ2χ2 =            

so (Click to select)RejectDo not reject H₀: independence

(b) Compute a 95 percent confidence interval for the difference between p₁ and p₄. (Round your answers to 3 decimal places. Negative amounts should be indicated by a minus sign.)

95% CI: [  , ]

1. A coin is tossed 3 times. Let x be the random discrete variable representing the number of times tails comes up.

a) Create a sample space for the event;   

b) Create a probability distribution table for the discrete variable x;                

c) Calculate the expected value for x.

2. For the data below, representing a sample of times (in minutes) students spend solving a certain Statistics problem, find P₃₅, range, Q₂ and IQR.

3.0, 3.2, 4.6, 5.2 3.2, 3.5

=> no handwriting. I can't read it correctly.

An article regarding interracial dating and marriage recently appeared in a newspaper. Of the 1708 randomly selected adults, 307 identified themselves as Latinos, 322 identified themselves as blacks, 255 identified themselves as Asians, and 777 identified themselves as whites. Among Asians, 79% would welcome a white person into their families, 71% would welcome a Latino, and 66% would welcome a black person. NOTE: If you are using a Student's t-distribution, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)

A. Construct the 95% confidence intervals for the three Asian responses. (Round your answers to four decimal places.)

Welcome a white person (_____,_______)

Welcome a Latino   (_____,_______)

Welcome a black person (_____,_______)

B. Even though the three point estimates are different, do any of the confidence intervals overlap? Which? (Select all that apply.)

Yes, the intervals for whites and Latinos overlap.

Yes, the intervals for Latinos and blacks overlap.

Yes, the intervals for whites and blacks overlap.

No confidence intervals overlap.

Yes, all three intervals overlap.

A sample of movie concessions purchases yielded the following:

27.50 18.65 12.10 36.45 19.50 21.40 28.70 14.55 7.60 43.50 23.25 17.60

a. what is the population mean guess

b. What is the standard deviation of the estimate for the population?

c. A 90% confidence interval will have a range of ?

d. A 95% confidence interval with have a value range of ?