A fair coin is flipped four times. What is the probability that tails occurs exactly 4 times if it is known that tails occurs at least twice

Mr. James McWhinney, president of Daniel-James Financial Services, believes there is a relationship between the number of client contacts and the dollar amount of sales. To document this assertion, Mr. McWhinney gathered the following sample information. The x column indicates the number of client contacts last month and the y column shows the value of sales ($ thousands) last month for each client sampled.

1. Determine the regression equation. (Negative values should be indicated by a minus sign. Do not round intermediate calculations. Round final answers to 2 decimal places.)

b. Determine the estimated sales if 40 contacts are made. (Do not round intermediate calculations. Round final answers to 2 decimal places.)

Demonstrate the use of the normal distribution, the standard normal distribution, and the central limit theorem for calculating areas under the normal curve and exploring these concepts in real life applications. Scenario Frank has only had a brief introduction to statistics when he was in high school 12 years ago, and that did not cover inferential statistics. He is not confident in his ability to answer some of the problems posed in the course. As Frank's tutor, you need to provide Frank with guidance and instruction on a worksheet he has partially filled out. Your job is to help him understand and comprehend the material. You should not simply be providing him with an answer as this will not help when it comes time to take the test. Instead, you will be providing a step-by-step breakdown of the problems including an explanation on why you did each step and using proper terminology. What to Submit To complete this assignment, you must first download the word document, and then complete it by including the following items on the worksheet: Incorrect Answers Correct any wrong answers. You must also explain the error performed in the problem in your own words. Partially Finished Work Complete any partially completed work. Make sure to provide step-by-step instructions including explanations. Blank Questions Show how to complete any blank questions by providing step-by-step instructions including explanations. Your step-by-step breakdown of the problems, including explanations, should be present within the word document provided. You must also include an Excel workbook which shows all your calculations performed.

You are working on a research team studying body size of Erissinettes, a newly discovered alien race on the exoplanet Eris. The weirdly adorable Erissinettes have antennae that help the organisms interact with their environment and agile tails used to trap unsuspecting humans for drippy cuddles. Due to their novelty and pleasing resemblance to earth canines, interest in Erissinette biology is high and research dollars are flowing. Your job is to catalog the complex traits of antennae length and tail length and see if there is a correlation. The hope is to selectively breed smaller Erissinettes for transport and sale on Earth. This plan ignores the research suggesting Erissinette brain biology is much more similar to Earth felines; making them extremely intelligent organisms with egomania and manipulative tendencies.

What are the average, median, mode, variance, and standard deviation of antennae length and tail length? Graph antennae length by tail length in a scatterplot. Does there appear to be a correlation between the two traits? Is the correlation positive or negative? Can you quantify the correlation?

Figure how to visually represent the mathematical value of the correlation on your chart. (See lung function example in lecture for an idea of what you could produce). Write step-by-step directions on how to do this in excel. There may be more than one method and type of correlation that would be an acceptable answer to this question. Fully explain the mathematical basis of what you did and how you did it.

A study is conducted for students taking a statistics class.  Several variables are recorded in the survey.  The 300 students were asked what type of car the student owns, the number of credit hours taken during that semester, the time the student waited in line at the bookstore to pay for his/her textbooks, and the home state of the students.  

1. Which of the following plots would be appropriate to graph the home states of the students?

bar graph, histogram, scatter plot, or side-by-side boxplot

2. The type of car a student owned was classified as an SUV, a sedan, or a sports car.  If the surveyors wanted to explore the relationship between type of car and the time the student waited in line at the bookstore, what plot would be most appropriate?

bar graph, histogram, scatter plot, or side-by-side boxplot

3. The mean number of credits taken during the semester by 300 surveyed students was 15.  The number 15

4. The number of credits taken during the semester for all students at Pitt is known to follow a Normal distribution with mean 14 and standard deviation 3. Based on the 68-95-99.7 rule, what proportion of students take more than 17 credits?

2.5%, 16%, 32%, or 95%

Algebra scores in a school district are normally distributed with a mean of 74 and standard deviation 6. A new teaching-and-learning system, intended to increase average scores, is introduced to a random sample of 30 students, and in the first year the average was 76.

(a) What is the probability that an average as high as 76 would have been obtained under the old system?

(b) What is the null hypothesis for testing the new system, and what is the alternative hypothesis?

(c) Is the test significant at the 0.05 level? What about the 0.01 level? Explain your answers.

3) As part of your work for an environmental awareness group, you want to test the claim that the mean amount of lead in the air in U.S. cities is less than 0.036 microgram per cubic meter. You find that the mean amount of lead in the air for a random sample of 56 U.S. cities is 0.039 microgram per cubic meter with a standard deviation of 0.069 microgram per cubic meter. At α = 0.01 what can be concluded about the claim?

One die is rolled and one marble – yellow, blue, purple, or red is selected at random.

-Determine the number of possible arrangements.

-Determine the probability of obtaining the number 2 and the blue marble.

-Determine the probability of obtaining the number 3 or the red marble.

-Determine the probability of obtaining an odd number or the purple marble.

Oxnard Petro, Ltd., has three interdisciplinary project development teams that function on an ongoing basis. Team members rotate from time to time. Every 4 months (three times a year) each department head rates the performance of each project team (using a 0 to 100 scale, where 100 is the best rating). Are the main effects significant? Is there an interaction?

  Click here for the Excel Data File

(a-1) Choose the correct row-effect hypotheses.

• a

• b

(a-2) Choose the correct column-effect hypotheses.

• a

• b

(a-3) Choose the correct interaction-effect hypotheses.

• a

• b

(b) Fill in the missing data. (Round your Table of Means values to 1 decimal place, SS and F values to 2 decimal places, MS values to 3 decimal places, and p-values to 4 decimal places.)

Cantor et al. (1988) reported a study of the relationship between the regular use of hair dye and the development of leukemia. The study entailed 577 leukemia patients and 1245 persons free from the disease (controls) who were questioned concerning their use of hair dye. Forty-three patients and 55 controls claimed to have had significant exposure to hair dye.

a. Carry out the chi-square test of significance to test hair dye use (rate) differences between cases and control.

b. Is there evidence of an association between the use of hair dye and the development of leukemia? If so, is the association true beyond chance?

5. The following is house price ($ thousands) and annual crime rate in different neighborhoods of a midwestern city 130 150 200 230 250 280 300 350 320 200 100 220 95 85 60 55 67 35 22 40 10 20 35 15 a. Write the linear regression equation b. Explain the intercept and the slope in practical terms c. How much of the variation in prices is explained by crime rate? d. Are we missing other important determinants of house price? like what?

    Records of 40 used passenger cars and 40 used pickup trucks were randomly sampled to investigate

          whether there was any significant difference in the mean time in years that they were kept by the original

          owner before being sold.  For the sampled cars, the mean was 5.3 years with a standard deviation of 2.2

          years.  For the sampled pickup trucks, the mean was 7.1 years with a standard deviation of 3.0 years.  

          (Assume that the two samples are independent.)

a)  Construct and interpret the 90% confidence interval estimate of the difference between the mean time for all passenger cars and the mean time for all pickup trucks.

b)  Does there appear to be a significant difference between the two population means?  Is one higher than

               the other?  If so, who keeps their vehicles longer?

Are you likely to purchase an item promoted by a celebrity on a social media​ site? According to a​ survey, 26​% of social media users have made such a purchase. Complete parts​ (a) through​ (d) below.

a. Suppose that the survey had a sample size of n =900. Construct a 90% confidence interval estimate for the population proportion of social media users that have purchased an item promoted by a celebrity on a social media site.

≤ π ≤

​(Type an integer or a decimal. Round to four decimal places as​ needed.)

b. Based on​ (a), can you claim that more than a quarter of all social media users have purchased an item promoted by a celebrity on a social media​ site?

c. Repeat parts​ (a) and​ (b), assuming that the survey had a sample size of n= 10,000

d. Discuss the effect of sample size on the confidence interval estimate

hey, how to solved the question such as "State which features are categorical". and "Which are the two most strongly correlated features? What is the numerical and/or statistical relationship between them?" for a dataset

Determine the margin of error for a confidence interval to estimate the population mean with nequals24 and s​ = 13.5 for the confidence levels below. ​a) 80​% ​b) 90​% ​c) 99​%