A random sample was selected to determine whether the gas fuel cost different between east side (consider as 1) and west side (consider as 2). Given α=0.05. The data are summarized below:

East Side West Side Difference

Average 2.90/gal                                       2.99/gal                                       -0.09/gal

Count 12                                                     12 12

Standard deviation 0.81                                                  0.95                                          0.38

(d) Is there sufficient evidence to indicate that the gas fuel cost different between east side and west side?

Group of answer choices

Yes

No

Taylor reads that 65% of men do not wassh their hands after going to the resteroom. He camps put in a restroom and randomly observes 40 men. Of these 40 men, 30 do not wash their hands. Is this a significantly different percentage at the 1% level of significance?

Consider the time series given by y_t = a₁y_t-1 + a₂y_t-2 + ε_t. Where ε_t is independent white noise and y_t is stationary.

A.    Compute the mean of y_t. E(y_t)

B.   Compute the variance of y_t. E[y_t − E(y_t)]²

C.    Compute the first three autocovariances for y_t. (E[(y_t −E(y_t))(y_t−i −E(y_t−i))] i=1,2,3).

2. A professor was curious as to whether the students in a very large class she was teaching, who turned in their tests first, scored differently from the class mean on the test. The μ on the test was 75 with σ = 10; the scores were approximately normally distributed. The mean score for the first 20 tests was 78. Did the students turning in their tests first score significantly different from the larger mean at the .05 level?

   a) Use the four steps of hypothesis testing b) Illustrate the distributions involved

   c) Calculate the 95% confidence interval (*even if ns result)

You have torn a tendon and are facing surgery to repair it. The surgeon explains the risks to you: infection occurs in 4% of such operations, the repair fails in 14%, and both infection and failure occur together in 2%. What percent of these operations succeed and are free from infection?

The scores 30 students earned on the Calculus I final exam are listed in the data set below (in percentage).

examscores=c(95,68,65,50,82, 85,91,83,70,67, 68,65,52,39,48, 75,65,70,68,65, 69,71,68,73,78, 80,51,65,64,87)

Include your R commands and output for each part of the problem.

a) Create a stem and leaf plot for this data.

b) Comment on at least three features of the distribution using statistical terminology.

c) One of the data values is 39%. Would that value be considered unusual? Show work to justify your answer.

d) One of the data values is 39%. Would that value be considered an outlier? Show work to justify your answer.

Recall the researcher who investigated the relationship between hours of sleep and reaction times in the Week 4 Application. As a follow up to that study, the researcher wants to conduct a correlation to investigate further if there is a relationship between hours of sleep and reaction time. For this experiment, participants are allowed to sleep as much as they would like (that is, they are not assigned to sleep any specific number of hours). When 20 participants come to their appointment time, they report to the researcher how many hours of sleep they had the previous night. The researcher then tests their reaction times.

data:

The risk of developing iron deficiency is especially high during pregnancy. Consider the following data on transferrin receptor concentration (mg/L) for a sample of women with laboratory evidence of overt iron-deficiency anemia. Please answer each question below showing all calculations by hand.

11.2, 10.5, 7.6, 11.3, 10.4, 9.7, 20.8, 9.4, 19.5, 9.4, 8.3

(a) What is the median transferrin receptor concentration for these 11 women?

(b) What is the mean transferrin receptor concentration for these 11 women?

(c) Do you regard the mean or the median as more representative of the center of the data? Explain your choice.

(d) What are the variance and standard deviation for transferrin receptor concentrations of these 11 women?

What is differences between a parameter and a random variable in statistics?

I want clear explanation !!

Using the mtcars dataset, answer the following questions:

Fill in the following table:

Which of the variables is the best predictor of mpg? Justify your answer using the correlation coefficient and a scatterplot.

Fit a regression model based on your answer to question 2. Write your model below.

Is the slope significant? Justify your answer.

Interpret the slope of your regression model.

Interpret the r² value.

Do you believe your model is a good model for predicting mpg? Justify your answer.

1. 100,000 Massachusetts adults were randomly sampled with two factors recorded: whether or not the individual

had diabetes, and whether or not the person ate Kale. The following gives a table of the results.

Diabetes No Diabetes

Kale: 796 9187

No Kale: 9900 80117

(a) We write p(Diabetes | Kale) for the probability that a Massachusetts adult who eats kale has diabetes.

Either give a value for p(Diabetes | Kale) or explain why it cannot be computed.

(b) We write ^p(Diabetes | Kale) for the proportion of Kale-eating members of our sample above that had

diabetes. Either give a value for ^p(Diabetes | Kale) or explain why it cannot be computed.

(c) Give 95% confidence intervals for the probability of having diabetes for both the kale-eating and non-kale-

eating members of our Massachusetts adults.

(d) Can you conclude that the kale-eaters are less likely to have diabetes? Explain your reasoning.

(e) Can you conclude that kale consumption causes a lower diabetes rate in this population? Explain your

reasoning.

(f) Come up with a possible theory that explains why kale-eaters have a lower rate of diabetes, but does not

assume that kale causes the lower rate.

I have no strong background in Probability, please, present to me an easy to understand solution to this problem with detail explanation. Thank you.

An urn contains three white, six red, and five black balls. Six of these balls are randomly selected from the urn. Let X and Y denote
respectively the number of white and black balls selected. Compute the conditional probability mass function of X given that Y = 3. Also compute E[X|Y = 1]

Describe and discuss at least 1 other business scenario in which you believe Chi-square testing would be helpful to a company.

Use the following data to conduct a Chi-square test for each region of the company

For 300 trading​ days, the daily closing price of a stock​ (in $) is well modeled by a Normal model with mean $195.89 and standard deviation ​$7.18

According to this​ model, what cutoff value of price would separate the

​a) lowest 15% of the​ days?

​b) highest 0.61​%?

​c) middle 80​%?

​d) highest 50​%?

c) Select the correct answer below and fill in the answer​ box(es) within your choice.

A.The cutoff points are _________ and _________.

​(Use ascending order. Round to two decimal places as​ needed.)

B.The cutoff point is _________. ​(Round to two decimal places as​ needed.)