Three different methods for assembling a product were proposed by an industrial engineer. To investigate the number of units assembled correctly with each method, 30 employees were randomly selected and randomly assigned to the three proposed methods in such a way that each method was used by 10 workers. The number of units assembled correctly was recorded, and the analysis of variance procedure was applied to the resulting data set.

The following results were obtained: SST = 10,840; SSTR = 4,580. Set up the ANOVA table for this problem (to 2 decimals, if necessary). Round p-value to four decimal places. Source of Variation Sum of Squares Degrees of Freedom Mean Square F p-value Treatments Error Total

Use = .05 to test for any significant difference in the means for the three assembly methods.

The p-value is

What is your conclusion?

Consider a large ferry that can accommodate cars and buses. The toll for cars is $3, and the toll for buses is $10. Let x and y denote the number of cars and buses, respectively, carried on a single trip. Cars and buses are accommodated on different levels of the ferry, so the number of buses accommodated on any trip is independent of the number of cars on the trip. Suppose that x and y have the probability distributions shown below:

(a) Compute the mean and standard deviation of x. (Round the answers to three decimal places.)
Mean of x
Standard deviation of x

(b) Compute the mean and standard deviation of y. (Round the answers to three decimal places.)
Mean of y
Standard deviation of y

(c) Compute the mean and variance of the total amount of money collected in tolls from cars. (Round the answers to two decimal places.)
Mean of the total amount of money collected in tolls from cars $
Variance of the total amount of money collected in tolls from cars

(d) Compute the mean and variance of the total amount of money collected in tolls from buses. (Round the answers to one decimal place.)
Mean of the total amount of money collected in tolls from buses $
Variance of the total amount of money collected in tolls from buses

(e) Compute the mean and variance of z = total number of vehicles (cars and buses) on the ferry. (Round the answers to two decimal places.)
Mean of z
Variance of z

(f) Compute the mean and variance of w = total amount of money collected in tolls. (Round the answers to one decimal place.)
Mean of w $
Variance of w

The amounts of electricity bills for all households in a particular city have approximately normal distribution with a mean of $140 and a standard deviation of $30. A researcher took random samples of 25 electricity bills for a certain study.

a. Based on this information, what is the expected value of the mean of the sampling distribution of mean?

b. What is the standard error of the sampling distribution of mean?

c. If his one sample of 25 bills has an average cost of $155, what is the z-score that represents the location of this value in the sampling distribution?

d. What is the probability of getting this result or greater (enter as a percentage - if your percentage is less than one full percent enter a zero before the decimal point)?

e. Assuming that z-scores greater than +2 or less than -2 are unlikely to occur due to sampling error alone, is this a likely or unlikely result?

What is the age distribution of patients who make office visits to a doctor or nurse? The following table is based on information taken from a medical journal.

Age group, years: Under 15, 15-24, 25-44, 45-64, 65 and older

Percent of office visitors: 15%, 10%, 25%, 15%, 35%

Suppose you are a district manager of a health management organization (HMO) that is monitoring the office of a local doctor or nurse in general family practice. This morning the office you are monitoring has eight office visits on the schedule. What is the probability of the following?

(a) At least half the patients are under 15 years old. (Round your answer to three decimal places.)

(b) From 2 to 5 patients are 65 years old or older (include 2 and 5). (Round your answer to three decimal places.) (c) From 2 to 5 patients are 45 years old or older (include 2 and 5). (Hint: Success if 45 or older. Use the table to compute the probability of success on a single trial. Round your answer to three decimal places.)

(d) All the patients are under 25 years of age. (Round your answer to three decimal places.)

(e) All the patients are 15 years old or older. (Round your answer to three decimal places.)

To illustrate the effects of driving under the influence​ (DUI) of​ alcohol, a police officer brought a DUI simulator to a local high school. Student reaction time in an emergency was measured with unimpaired vision and also while wearing a pair of special goggles to simulate the effects of alcohol on vision. For a random sample of nine​ teenagers, the time​ (in seconds) required to bring the vehicle to a stop from a speed of 60 miles per hour was recorded. Complete parts​ (a) and​ (b). ​Note: A normal probability plot and boxplot of the data indicate that the differences are approximately normally distributed with no outliers.

Subject   Normal, Xi   Impaired, Yi
1   4.47   5.86
2   4.24   5.67
3   4.58   5.45
4   4.56   5.32
5   4.31   5.90
6   4.83   5.49
7   4.55   5.23
8   5.00   5.61
9   4.79   5.63

​(a) Whether the student had unimpaired vision or wore goggles first was randomly selected. Why is this a good idea in designing the​ experiment?

A.

This is a good idea in designing the experiment because the sample size is not large enough.

B.

This is a good idea in designing the experiment because it controls for any​ "learning" that may occur in using the simulator.

C.

This is a good idea in designing the experiment because reaction times are different.

​(b) Use a​ 95% confidence interval to test if there is a difference in braking time with impaired vision and normal vision where the differences are computed as​ "impaired minus​ normal."

The lower bound is __?__.

The upper bound is __?__.

​(Round to the nearest thousandth as​ needed.)

State the appropriate conclusion. Choose the correct answer below.

There is insufficient evidence to conclude there is a difference in braking time with impaired vision and normal vision.

There is sufficient evidence to conclude there is a difference in braking time with impaired vision and normal vision.

Two assemblages of lithic scrapters were excavated from different levels in a cave site

Level 1:

Sample mean: 14.83

Variance: 7.05

Sample Size: 63

Level 2:

Sample Mean: 14.17

Variance: 5.49

Sample Size: 47

From superficial examination, they seem to differ. However, your job is to test whether the difference between the samples from the two levels represent a significant difference between the two occupations. Lets use a 0.05 significance level for this analysis

Step 1: Frame this is a way amenable to testing, with both research and null hypotheses.  

Step 2: Calculate the pooled standard error of means

Step 3: Calculate the t value

Step 4: Calculate the degrees of freedom, and find the corresponding critical t-value from a t-table (keep in mind that we are using the two-tailed test).

Step 5: Compare the calculated and critical values. What is your conclusion?  

Instructions: You are not required to use R markdown for the lab assignment. Please include ALL R commands you used to reach your answers in a word or pdf document. Also, report everything you are asked to do so.

Problem 1 : Consider a binomial random variable X ∼ Bin(100, 0.01). 1. Report P(X = 7), P(X = 8), P(X = 9), try to use one ONE R command to return all these three values. 2. Find the probability P(0 ≤ X < 5), be careful when treating “end points” 0 and 5. 3. We have mentioned on the class Possion distribution could be a good approximation of Binomial distribution under certain conditions. Here, n = 100, p = 0.01, np = 1 looks satisfy the condition that the pmf of X can be approximated by a suitable Possion random variable Y . What is λ of Y ? Compute P(X = i), P(Y = i), i = 0, 1, 2, 3, 4, 5 to show the goodness of the approximation.

Problem 2 : Answer the following questions: 1. First run alphas <- seq(0.1, 1, by = 0.1) and nalphas <- - rev(alphas). Based on what you have seen, decribe how functions seq and rev work. Then run qnorm(c(nalphas, alphas)) and report the result you get. What are they? What pattern did you notice and why? 2. Use the function rnorm to genearate 10000 random numbers from N(50, 4), store those random numbers into a vector called firstrn. It is expected that the sample mean of firstrn should be close to the population mean 50. Use the function mean to verify this. 3. Suppose X ∼ Possion(2). Report the probability that P(1 < X ≤ 5). Show the code you used to reach this answer.

Problem 3 : In lab lecture notes and demo code, I simulated random samples from Exp(1) to verify classical central limit theorem numerically. I also stressed that no matter what type of random samples you use, the standardized partial sum Sn always converge to N(0, 1). In this problem, simulate random samples from the following distributions: 1. Bernoulli(0.5) with µ = 0.5 and σ2 = 0.25. (Hint: You can use rbinom to generate Bernoulli random numbers.) 1 2. Uniform(0, 1) with µ = 0.5 and σ2 = 1/12. 3. Possion(1) with µ = 1 and σ2 = 1. For each case, set simulation times N to be 1000 and for each simulation, generate n = 2000 random numbers. Report 3 pieces of code, 3 Q-Q plots and your conclusion. To get all the answers, you only need slightly adjust my demo code

What does it mean for a hypothesis test to be statistically significant? How is this different from our everyday notions of “significant”? Make sure that you respond to your classmates as well.

A corporation is considering a new issue of convertible bonds. Management believes that the offer terms will be found attractive by 20% of all its current stockholders. Suppose that this belief is correct. A random sample of 130 current stockholders is taken. a. What is the standard error of the sample proportion who find this offer attractive? b. What is the probability that the sample proportion is more than 0.15? c. What is the probability that the sample proportion is between 0.18 and 0.22?

provide a step-by-step explanation

A sample on nine public universities and nine private universities was taken. The total cost for the year (including room and board) and median SAT score (maximum total is 2400) at each school were recorded. It was felt that schools with higher median SAT scores would have a better reputation and would charge more tuition as a result of that. The data is in the table below. Uss regression to help answer the following questions based on this sample data. Do schools with higher SAT scores charge more in tuition and fees? Are private schools more expensive than public school when SAT scores are taken into consideration.

Category              Total cost                             Median SAT

Public                   21,700                                  1990

Public                   15,600                                   1620

Public                   16,900                                   1810

Public                    15,400                                  1540

Public                    23,100                                   1540

Public                     21,400                                  1600

Public                     16,500                                   1560

Public                     23,500                                   1890

Public                     20,200                                    1620

Private                    30,400                                     1630

Private                    41,500                                    1840

Private                    36,100                                     1980

Private                    42,100                                     1930

Private                     27,100                                    2130

Private                     34,800                                    2010

Private                     32,100                                    1590

Private                     31,800                                    1720

Private                      32,100                                    1770

PLEASE READ: PLEASE SHOW STOP BY STEP HOW YOU GOT THE ANSWER AND PLEASE SHOW HOW TO DO IT STEP BY STEP ON EXCEL. (answer will be thumbed down if this isn't included)

What is the​ p-value if, in a​ two-tail hypothesis​ test, Upper Z Subscript STATequalsplus1.43​? With Excel commands please

A population has a mean of 433 and a standard deviation of 102. If a sample of size 10 is taken, what is the probability the sample mean is greater than 472.2? Enter your answer as a decimal to 3 decimal places

A population has a mean of 218 and a standard deviation of 133. If a sample of size 8 is taken, what is the probability the sample mean is greater than 115.7 but less than 228.8? Enter your answer as a decimal to 3 decimal places.

A population has a mean of 161.2 and a standard deviation of 9.6. A sample of size 13 is taken from this population. What is the standard deviation of the sampling distribution of the mean?  Enter your answer to 3 decimal places.

We have two random variables, A and B. A has a mean of 74.6 and a standard deviation of 36.4. B has a mean of 35.7 and a standard deviation of 19.4. If we create a new random variable C, defined as C= A + B, what is the mean of C? Enter your answer as a decimal to one decimal place.

The length of time for one individual to be served at a cafeteria is a random variable having an exponential distribution with a mean of 5 minutes. What is the probability that a person is served in less than 2 minutes on at least 5 of the next 7 days?

1. You do a study on participation in sports and good or bad health. You find out only 1 person in your study had poor health and participated in sports.

What test should you use?

1. Chi-Squared
2. Fisher Exact test
3. McNemar test
4. All of the above