Question 3:

In “Orthogonal Design for Process Optimization and Its Application to Plasma Etching”, an experiment is described to determine the effect of flow rate on the uniformity of the etch on a silicon wafer used in integrated circuit manufacturing. Three flow rates are used in the experiment, and the resulting uniformity (in percent) for six replicates is shown below.

1. Does flow rate affect etch uniformity? Use α = 0.05.
2. Do the residuals indicate any problems with the underlying assumptions?
3. Use the Kruskal-Wallis procedure with α = 0.05 to test for differences between mean uniformity at the three different flow rates.

"Black Friday" is the day after Thanksgiving and the traditional first day of the Christmas shopping season. Suppose a recent poll suggested that 66% of Black Friday shoppers are actually buying for themselves. A random sample of 130 Black Friday shoppers is obtained. Answer each problem using the normal approximation to the binomial distribution.

(a)

Find the approximate probability that fewer than 73 Black Friday shoppers are buying for themselves. (Round your answer to four decimal places.)

(b)

Find the approximate probability that between 74 and 84 (inclusive) Black Friday shoppers are buying for themselves. (Round your answer to four decimal places.)

We throw a die independently four times and let X denote the minimal value rolled. (a) What is the probability that X ≥ 4. (b) Compute the PMF of X. (c) Determine the mean and variance of X.

5.
a. Analyze the Bread variable in the SandwichAnts dataset using aov() in R and
interpret your results.
The data may be found here:
install.packages("Lock5Data")
library(Lock5Data)
data(SandwichAnts,package="Lock5Data")
attach(SandwichAnts)
b. State the linear model for this problem. Define all notation and model terms.
c. Create the design matrix for this problem.
d. Estimate model parameters for this problem using ? = (?^T?)^-1?^T?
e. Interpret the meaning of the estimates from part d.
f. Rerun this problem using lm()in R. Interpret the coefficients in the output.
g. Rewrite the model in as a linear regression using dummy variables. Confirm the
results from part f. agree with the results from part g.
h. Perform a one-way ANOVA of Bread using a randomization test on the
SandwichAnts dataset.

Two successive flips of a fair coin is called a trial. 100 trials are run with

a particular coin; on 22 of the trials, the coin comes up “heads” both

times; on 60 of the trials the coin comes up once a “head” and once a

“tail”; and on the remaining trials, it comes up “tails” for both flips. Is this

sufficient evidence ( = : 05) to reject the notion that the coin (and the

flipping process) is a fair one?

(Hint: chi sq)

Find the indicated probabilities using the geometric​ distribution, the Poisson​ distribution, or the binomial distribution. Then determine if the events are unusual. If​ convenient, use the appropriate probability table or technology to find the probabilities.

The mean number of oil tankers at a port city is

1313

per day. The port has facilities to handle up to

1717

oil tankers in a day. Find the probability that on a given​ day, (a)

thirteenthirteen

oil tankers will​ arrive, (b) at most three oil tankers will​ arrive, and​ (c) too many oil tankers will arrive.

FORECASTING , THE COMPLETE ANSWERS TO THESE QUESTIONS WILL RECEIVE A THUMBS UP!

Weekly demand figures at Hot Pizza are as follows:

Estimate demand for the next 4 weeks using a 4-week moving average as well as simple exponential smoothing with α = 0.1. Evaluate the MAD, MAPE, MSE, bias, and TS in each case. Which of the two methods do you prefer? Why?

For the Hot Pizza data in Exercise 2, compare the performance of simple exponential smoothing with α = 0.1 and α = 0.9. What difference in forecasts do you observe? Which of the two smoothing constants do you prefer?

I NEED ALL THE ERRORS , FOR MOVING AVERAGE AND EXPONENTIAL SMOOTHING AND THE 4 WEEK FORECAST RESULTS , THANK YOU , THE ANSWERS TO THE QUESTIONS!!!!!

A clinical trial was conducted to test the effectiveness of a drug for treating insomnia in older subjects. Before​ treatment, 20 subjects had a mean wake time of 105.0 min. After​ treatment, the 20 subjects had a mean wake time of 98.5 min and a standard deviation of 21.52 min. Assume that the 20 sample values appear to be from a normally distributed population and construct a 95​% confidence interval estimate of the mean wake time for a population with drug treatments. What does the result suggest about the mean wake time of 105.0 min before the​ treatment? Does the drug appear to be​ effective? Construct the 95​% confidence interval estimate of the mean wake time for a population with the treatment.

Starting salaries of 110 college graduates who have taken a statistics course have a mean of $43,598. Suppose the distribution of this population is approximately normal and has a standard deviation of $8,635.
Using a 93% confidence level, find both of the following:

(a) The margin of error:  

(b) The confidence interval for the mean μ:

  <. ? <

Problem 4) Five coins are flipped. The first four coins will land on heads with probability 1/4. The fifth coin is a fair coin. Assume that the results of the flips are independent. Let X be the total number of heads that result.

(hint: Condition on the last flip).

a) Find P(X=2)

b) Determine E[X]

Do college students enjoy playing sports more than watching sports? A researcher randomly selected ten college students and asked them to rate playing sports and watching sports on a scale from 1 to 10 with 1 meaning they have no interest and 10 meaning they absolutely love it. The results of the study are shown below.

Assume a Normal distribution. What can be concluded at the the αα = 0.10 level of significance level of significance?

For this study, we should use Select an answerz-test for the difference between two population proportionst-test for the difference between two dependent population meansz-test for a population proportiont-test for the difference between two independent population meanst-test for a population mean

1. The null and alternative hypotheses would be:   
2.   

H0:H0:  Select an answerp1μdμ1 ?=>≠< Select an answer0μ2p2 (please enter a decimal)   

H1:H1:  Select an answerμdμ1p1 ?<=>≠ Select an answerp20μ2 (Please enter a decimal)

2. The test statistic ?zt = (please show your answer to 3 decimal places.)
3. The p-value = (Please show your answer to 4 decimal places.)
4. The p-value is ?≤> αα
5. Based on this, we should Select an answerfail to rejectrejectaccept the null hypothesis.
6. Thus, the final conclusion is that ...
   • The results are statistically insignificant at αα = 0.10, so there is insufficient evidence to conclude that the population mean rating for playing sports is greater than the population mean rating for watching sports.
   • The results are statistically insignificant at αα = 0.10, so there is statistically significant evidence to conclude that the population mean rating for playing sports is equal to the population mean rating for watching sports.
   • The results are statistically significant at αα = 0.10, so there is sufficient evidence to conclude that the ten students that were surveyed rated playing sports higher than watching sports on average.
   • The results are statistically significant at αα = 0.10, so there is sufficient evidence to conclude that the population mean rating for playing sports is greater than the population mean rating for watching sports.

Your friend’s professor gives out reasonably hard exams 70% of the time, and ridicu- lously hard exams 30% of the time. On hard exams, each student’s score on the exam is a normally distributed random variable with μH = 70 and σH = 10. On ridiculously hard exams, each student’s score on the exam is a normally distributed random variable with μR = 50 and σR = 15. Suppose you have four friends in the class, not just one. Let A be the average score of your four friends: A= (F1 +F2 +F3 +F4)/ 4 Where F1 is your first friend’s score, and F2 is your second friend’s score. Find E[A] and V ar(A) if the exam is ridiculously hard. (e) Find E[A] and V ar(A) if the exam is reasonably hard. (f) Since A is the sum of normal random variables, it is itself a normal random variable. Find P (A > 65) if the exam is reasonably hard, and if it is ridiculously hard. (g) If A is greater than 65, what is the probability the exam was ridiculously hard?

The yield of Australia bank stocks has a normal distribution with s.d. 0.024. A random sample of 10 Australian bank stocks gave the mean yield 0.0538. For the entire Australia stock market, the mean dividend yield is 0.047. Does this indicate that the dividend yield of all Australia bank stock is higher than 0.047? Let alpha = .01, do a hypothesis test.

a. test statement: null/alternative

b. calculate test statistic.

c. Find the critical value and draw a graph to find the reject region. Then make your decision.

d. Find the p value and draw a graph to mark the p value. Then make your decision.

e. Give your conclusion in a way that non-staticians can understand.

Let X₁,X₂,...X_n be a random sample of size n form a uniform distribution on the interval [θ₁,θ₂]. Let Y = min (X₁,X₂,...,X_n).

(a) Find the density function for Y. (Hint: find the cdf and then differentiate.)

(b) Compute the expectation of Y.

(c) Suppose θ₁= 0. Use part (b) to give an unbiased estimator for θ₂.