Suppose you have a connected network of two-way streets. Show that you can drive along these streets so that you visit all streets and you drive along each side of every street exactly once. Further, show that you can do this such that, at each intersection, you do not leave by the street you first used to enter that intersection unless you have previously left via all other streets from that intersection

​a) Find the mean and standard deviation for the random variable X-11.

1. A soccer player will kick a ball 80 times during practice. Assume that the kicks are independent of each
other, and the probability that he scores is 0.6 (60% chance that the ball goes into the goalpost and 40%
chance that the ball does not go into the goalpost).
Let X be the number of successful goals (number of scores) out of the 80 kicks.
(a) What is the distribution of X?
(b) Write the pmf f(x) and name its parameters.
(c) What key assumption of the kicks is needed to determine this distribution?
(d) What is the expected number of kicks that go into the goalpost? Interpret this value for the soccer
player (in a sentence or two).
(e) What is the expected number of kicks that do not go into the goal post? Interpret this value for
the soccer player (in a sentence or two).
(f) Say each kick is blocked by the opponent goal keeper 30% of the time regardless of whether the ball
was going in or out of the goalpost. What is the expected number of blocks? What is the variance
of the number of blocks?
(g) Now say each kick that was supposed to go into the goal post is rebounded by another player 50%
of the time and each kick that was not going into the goalpost is rebounded by another player 10%
of the time. What is the expected number of rebounds?

Using minitab, how do you know whether or not to reject the null hypothesis when you are doing a chi-square test for differences among more than two proportions?

PLEASE SHOW HOW TO SOLVE IN EXCEL SHOW STEPS

Refer to the Johnson Filtration problem introduced in this section. Suppose that in addition to information on the number of months since the machine was serviced and whether a mechanical or an electrical repair was necessary, the managers obtained a list showing which repairperson performed the service. The revised data follow.

1. Ignore for now the months since the last maintenance service (x₁) and the repairperson who performed the service. Develop the estimated simple linear regression equation to predict the repair time (y) given the type of repair (x₂). Recall that x₂ = 0 if the type of repair is mechanical and 1 if the type of repair is electrical.
2. Does the equation that you developed in part (a) provide a good fit for the observed data? Explain.
3. Ignore for now the months since the last maintenance service and the type of repair associated with the machine. Develop the estimated simple linear regression equation to predict the repair time given the repairperson who performed the service. Let x₃ = 0 if Bob Jones performed the service and x₃ = 1 if Dave Newton performed the service.
4. Does the equation that you developed in part (c) provide a good fit for the observed data? Explain.
5. Develop the estimated regression equation to predict the repair time given the number of months since the last maintenance service, the type of repair, and the repairperson who performed the service.
6. At the .05 level of significance, test whether the estimated regression equation developed in part (e) represents a significant relationship between the independent variables and the dependent variable.
7. Is the addition of the independent variable x₃, the repairperson who performed the service, statistically significant? Use α = .05. What explanation can you give for the results observed?

You know that y is a normally distributed variable with a variance of 9. You do not know its mean. You collect some data. For each sample below, form the 95% confidence interval and test the null hypothesis of the mean equaling 2.

a. (8,1,5)

b. (8,1,5,-4,-8)

c. (8,1,5,-4,-8,4,8,5)

You are given the sample mean and the population standard deviation. Use this information to construct the​ 90% and​ 95% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals. If​convenient, use technology to construct the confidence intervals.

A random sample of 50 home theater systems has a mean price of ​$130.00. Assume the population standard deviation is $15.50.

Construct a​ 90% confidence interval for the population mean.

The​ 90% confidence interval is __,__

Determine the sampling method used in the following scenarios and state whether it is generally biased, or generally unbiased. If a method is generally biased give a reason why it may be biased. a. A factory uses three machines to make a product and the output follows a pattern of Machine 1, Machine 2, Machine 3, Machine 1, … To collect a sample one of the first three products in the line is selected and then every 10th product is selected. b. In order to complete an assignment in a statistics class, a student surveys 15 of their friends. c. A sports talk show posts a poll on their website on the topic they are discussing that day. d. In a clinical trial an independent company is hired to administer a drug trial. 100 people are selected to participate in the trial and split into two groups of 50. One group of 50 is given the medication, and the other 50 are given sugar pills (placebo). The participants and the person administering the “medication” do not know if they are in the test group, or the placebo group.

We had an example in class about using a sign test. We are supposed to find the b value by using the binomial table. b(alpha,n,1/2) which for this problem equals b(.05,10,1/2). When you use the binomial table, the b(.05,10,1/2) = 8. How do you use the binomial table to get 8 for the b value?

Using the unit normal table, find the proportion under the standard normal curve that lies between the following values. (Round your answers to four decimal places.) (a) the mean and z = 0 (b) the mean and z = 1.96 (c) z = −1.20 and z = 1.20 (d) z = −0.80 and z = −0.70 (e) z = 1.00 and z = 2.00

Please read through the entire question before answering. I'm asking for assistance on how to calculate LOSS, not gain. Thank you!

The major stock market indexes had strong results in 2014. The mean one-year return for stocks in the S&P 500, a group of 500 very large companies was +11.4%. The mean one year return for the NASDAQ, a group of 3200 small and medium-sized companies was +13.4%. Historically, the one-year returns are approximately normal, the standard deviation in the S&P 500 is approximately 20% and the standard deviation in NASDAQ is approximately 30%.

1. What is the probability that a stock in the S&P 500 lost 20% or more in 2014?
2. What is the probability that a stock in the S&P 500 lost 30% or more in 2014?
3. Repeat for a stock in the NASDAQ.
4. Write a short report on your findings Be sure to include a discussion on the risks associated with a large standard deviation. How would you use the findings to provide advice on investing in the S&P 500 or NASDAQ stock market?  

A recent study found that 51 children who watched a commercial for Walker Crisps featuring a long-standing sports celebrity endorser ate a mean of 36 grams of Walker Crisps as compared toa mean of 25 grams of Walker Crisps for 41 Children who watched a commercial for alternative food snack. Suppose that the sample standard deviation for the children who watched the sports celebrity-endorsed Walker Crisps commercial was 21.4 grams and the sample standard deviation for the children who watched the alternative food snack commercial was 12.8 grams. Assuming the population variances are NOT equal and alpha=.05, is there any evidence that the mean amount of Walker Crisps eaten was significantly higher for the children who watched the sports celebrity endorsed Walker Crisps commercial?

1. What is the claim from the question? What are Null and Alternative Hypothesis for this problem?

2. What kind of test do you want to use? One Sample or Two Sample? Z test or T Test? One-tail or Two-tail test?

3. Calculate Test Statistics

4. Find Critical Value(s) and appropriate degree of freedom if necessary Critical Value(s): Test Statistics:

5. Find P-value

6. What is the conclusion that you could make? Clearly write down the conclusion and business statement and illustrate what type error you could make.

The vendor at Citi Field offers a health pack consisting of apples and oranges. The weight, X, of an apple has a normal distribution with a mean of 9 ounces and a standard deviation of 0.6 ounces. Independent of this, the weight, Y, of an orange has a normal distribution with a mean of 7 ounces and a standard deviation of 0.4 ounces. Suppose the health pack has a random selection of 4 apples with weights

X₁, X₂, X₃, X₄

and 3 oranges with weights

Y₁, Y₂, Y₃

. . Let Xsum be the sum of the apple weights in ounces and let Ysum be the sum of the orange weights in ounces. W = Xsum + Ysum is the random variable representing the total weight of the health pack.


a) What is the probability that Xsum > 38?  

b) What is the probability that Ysum > 22?  

c) What is the expected value of Xsum?  

d) What is the standard deviation of Xsum?  

e) What is the variance of the random variable W?  

f) What is the expected value of W?  

g) What is the standard deviation of W?  

h) What is the probability that W > 59 ounces?  

i) i. If 100 health packs are sold what is the expected number sold which weigh more than 59 ounces?

The monthly value of sales for the first 3 years of a restaurant’s operation is shown below (values are in 1,000 USD).

Use a multiple linear regression model with dummy variables to develop an equation to account for seasonal effect in the data. (data below) ---- SHOW IN EXCEL