An Internet user wants to know the average download speed for his Internet connection. Suppose we know that the standard deviation is 7 mbps. He runs a speed test everyday at noon for 30 days. The average speed of the tests was 13.68 mbps. Construct a 95% confidence interval for the average speed of this Internet connection at noon.

A)Let S = {1,2,3,...,18,19,20} be the universal set.

Let sets A and B be subsets of S, where:

Set A={3,4,9,10,11,13,18}A={3,4,9,10,11,13,18}

Set B={1,2,4,6,7,10,11,12,15,16,18}B={1,2,4,6,7,10,11,12,15,16,18}

LIST the elements in Set A and Set B: {  }

LIST the elements in Set A or Set B: {  }

B)A ball is drawn randomly from a jar that contains 4 red balls, 5 white balls, and 9 yellow balls. Find the probability of the given event. Write your answers as reduced fractions or whole numbers.

(a) PP(A red ball is drawn) =    

(b) PP(The ball drawn is NOT red) =    

(c) PP(A green ball is drawn) =  

C)

As part of a statistics project, a teacher brings a bag of marbles containing 700 white marbles and 400 red marbles. She tells the students the bag contains 1100 total marbles, and asks her students to determine how many red marbles are in the bag without counting them.

A student randomly draws 100 marbles from the bag. Of the 100 marbles, 41 are red.

The data collection method can best be described as?

• Census
• Survey or Sample
• Controlled study
• Clinical study

The target population consists of?

• The 1100 marbles in the bag
• The 41 red marbles drawn by the student
• The 100 marbles drawn by the student
• The 400 red marbles in the bag
• None of the above

The sample consists of?

• The 41 red marbles drawn by the student
• The 1100 marbles in the bag
• The 100 marbles drawn by the student
• The 400 red marbles in the bag
• None of the above

The following indicates the number of hours that Johnny spent studying the week before each exam in his classes along with the corresponding exam scores:
Hours Studying:  4    5    8  12  15  19
Score on Exam:  54  49 60  70  81 94

Find the residual corresponding to the explanatory value of 8.

a) 69.8263

b) −0.82

c) −69.8263

d) −126.34

e) 0.82

Twenty people check their hats at a theater. In how many ways can their hats be returned so that

(a) no one receives his or her own hat?

(b) at least one person receives his or her own hat?

(c) exactly one person receives his or her own hat?

Athletes performing in bright sunlight often smear black eye grease under their eyes to reduce glare. In one study, 16 student subjects took a test of sensitivity to contrast after three hours facing into bright sun, both with and without eye grease. This is a matched-pair design. Here are the differences in sensitivity, where the difference is defined as eye grease minus without eye grease:

0.07,0.64, -0.12, -0.05, -0.18, 0.14, -0.16, 0.03, 0.05, 0.02, 0.43, 0.24, -0.11, 0.28, 0.05, 0.29

Does eye grease work? Let m be the mean sensitivity difference in the population. We want to know whether eye grease increases sensitivity, on the average (i.e., m > 0).

(A) State the null and alternative hypotheses.

(B) Assume that the “simple conditions” hold. Suppose that the subjects are an SRS of all young people with normal vision, that contrast differences follow a Normal distribution in this population, and that the standard deviation of differences is St dev = 0.22. Carry out a test of significance at the a = 0.05 level by following the State, Plan, Solve, and Conclude of the four-step process.

Vigorous exercise is associated with several years of longer life (on the average). Whether mild activities like slow walking are associated with a longer life is not clear. Suppose that the added life expectancy associated with slow walking daily for 10 minutes is just one month. A statistical test is more likely to find a significant increase in mean life for those who slow walk daily if

(A) it is based on a very large random sample.

(B) it is based on a very small random sample.

(C) the size of the sample has little effect on significance for such a small increase in life expectancy

a) Calculate mean duration and standard deviation for all the activities using the beta distribution. [4pts]
  
b) Construct a network diagram for this problem using the mean durations calculated in part (a), calculate the LS(Foll.), ES(Prec.) and total float for all the activities, and hence identify the critical path . What is the mean completion time for the project? What is the standard deviation of the critical path? [30 pts ]
  
c) What is the 92% confidence interval for the length of the critical path? [4 pts]
  
d) Assuming the probability distribution of the length of the critical path can be approximated by a normal distribution with the mean and standard deviation calculated in part (b), calculate the probability of completing the project within 42 weeks. [4 pts]

e) Calculate the probability of completing the project between 35 and 40 weeks? [4 pts]
  
f) Answer the project manager’s question: “I want to tell the client that there is a 10.03% chance the project will take longer than X weeks _{- what figure should I give them (i.e. find X)?” [4]}

(please show work step by step and excel file)

1. A survey was conducted to investigate motor fuel octane ratings of several blends of gasoline, and the following data is presented:

1. Construct stem-and-leaf diagram for these data and compute the sample quartiles. (10 pts)
2. Compute sample median, mode, mean, variance and standard deviation. (5 pts)
3. Construct a frequency distribution and histogram for the ratings by using eight bins. What is the shape of the distribution? (10 pts)

On Excel

Purpose of Assignment

The purpose of the assignment is to develop students' abilities in using data sets to apply the concepts of sampling distributions and confidence intervals to make management decisions.

Assignment Steps

Resources: Microsoft Excel®, The Payment Time Case Study, The Payment Time Case Data Set

Review the Payment Time Case Study and Data Set.

Develop a 700-word report including the following calculations and using the information to determine whether the new billing system has reduced the mean bill payment time:

• Assuming the standard deviation of the payment times for all payments is 4.2 days, construct a 95% confidence interval estimate to determine whether the new billing system was effective. State the interpretation of 95% confidence interval and state whether or not the billing system was effective.
• Using the 95% confidence interval, can we be 95% confident that µ ≤ 19.5 days?
• Using the 99% confidence interval, can we be 99% confident that µ ≤ 19.5 days?
• If the population mean payment time is 19.5 days, what is the probability of observing a sample mean payment time of 65 invoices less than or equal to 18.1077 days?

Case Study – Payment Time Case Study

Major consulting firms such as Accenture, Ernst & Young Consulting, and Deloitte & Touche Consulting employ statistical analysis to assess the effectiveness of the systems they design for their customers. In this case, a consulting firm has developed an electronic billing system for a Stockton, CA, trucking company. The system sends invoices electronically to each customer’s computer and allows customers to easily check and correct errors. It is hoped the new billing system will substantially reduce the amount of time it takes customers to make payments. Typical payment times—measured from the date on an invoice to the date payment is received—using the trucking company’s old billing system had been 39 days or more. This exceeded the industry standard payment time of 30 days.

The new billing system does not automatically compute the payment time for each invoice because there is no continuing need for this information. The management consulting firm believes the new system will reduce the mean bill payment time by more than 50 percent. The mean payment time using the old billing system was approximately equal to, but no less than, 39 days. Therefore, if µ denotes the new mean payment time, the consulting firm believes that µ will be less than 19.5 days. Therefore, to assess the system’s effectiveness (whether µ < 19.5 days), the consulting firm selects a random sample of 65 invoices from the 7,823 invoices processed during the first three months of the new system’s operation. Whereas this is the first time the consulting company has installed an electronic billing system in a trucking company, the firm has installed electronic billing systems in other types of companies.

Analysis of results from these other companies show, although the population mean payment time varies from company to company, the population standard deviation of payment times is the same for different companies and equals 4.2 days. The payment times for the 65 sample invoices are manually determined and are given in the Excel^® spreadsheet named “The Payment Time Case”. If this sample can be used to establish that new billing system substantially reduces payment times, the consulting firm plans to market the system to other trucking firms.

I do not need help with the paper. I need to understand the math.

A study was conducted to determine the proportion of people who dream in black and white instead of color. Among 312 people over the age of​ 55, 75 dream in black and​ white, and among 296 people under the age of​ 25, 16 dream in black and white. Use a 0.05 significance level to test the claim that the proportion of people over 55 who dream in black and white is greater than the proportion for those under 25. Complete parts​ (a) through​ (c) below.

a.) Identify the test statistic: z=_______; Identify the P-value: P-value=______

What is the conclusion based on the hypothesis test?

The P-value is ______ the significance level of alpha=0.05, so ______ the null hypothesis. There is _____ evidence to support the claim that the proportion of people over 55 who dream in black and white is greater than the proportion of those under 25.

b. Test the claim by constructing an appropriate confidence interval.

The 90% confidence interval is ____ < (p₁-p₂) < ______

What is the conclusion based on the confidence interval?

Because the confidence interval limits _____ 0, it appears that the two proportions are ________. Because the confidence interval limits include _____ values, it appears that the proportion of people over 55 who dream in black and white is ______ proportion of those under 25.  

c. What is an explanation for the results is that those over the age of 55 grew up exposed to media that was displayed in black and white. Can these results be used to verify that explanation?

The table below summarizes the replies of 300 randomly selected university graduates who participated in a nationwide survey:

(a) Determine the expected numbers, assuming the degree of job satisfaction is independent of type of program taken at university (i.e. there is some association between degree of job satisfaction and the type of program). Fill your answers into the table above.

(b) Use the Chi-square test with α = 0:05 to test the hypothesis that the degree of job satisfaction depends on the type of program taken at university.

i) H₀:

H_a:

Observed Test Statistic (x² statistic):

ii) p-value (use x² table):

Decision with justification:

Conclusion in context:

The empirically established mean score for sales for a population in a public company is 850. The scores for selected sales representatives,Ekle, Joshua and Keeble are 780, 700, and 810,respectively. Also considered are Roll, Jill, and Jan. Their scores are 680, 590 and 780,respectively. The Sales Division argues that these scores appear to be different from expectation. Assume the level of significance is 5%. Test the hypothesis that the representatives are not statistically different from expectation. Use the correct steps in testing a hypothesis

The null and alternate hypotheses are: H0: μ1 ≤ μ2 H1: μ1 > μ2 A random sample of 24 items from the first population showed a mean of 113 and a standard deviation of 13. A sample of 18 items for the second population showed a mean of 103 and a standard deviation of 14. Use the 0.05 significant level.

a. Find the degrees of freedom for unequal variance test. (Round down your answer to the nearest whole number.)

b. State the decision rule for 0.050 significance level. (Round your answer to 3 decimal places.)

c. Compute the value of the test statistic. (Round your answer to 3 decimal places.)

d. What is your decision regarding the null hypothesis? Use the 0.05 significance level.

Is there a relationship between confidence intervals and two-tailed hypothesis tests? Let c be the level of confidence used to construct a confidence interval from sample data. Let α be the level of significance for a two-tailed hypothesis test. The following statement applies to hypothesis tests of the mean.

For a two-tailed hypothesis test with level of significance α and null hypothesis H₀: μ = k, we reject H₀ whenever k falls outside the c = 1 –  α confidence interval for μbased on the sample data. When k falls within the c = 1 –  α confidence interval, we do not reject H₀.

(A corresponding relationship between confidence intervals and two-tailed hypothesis tests also is valid for other parameters, such as p, μ₁ − μ₂, or p₁ − p₂, which we will study in later sections.) Whenever the value of k given in the null hypothesis falls outside the c = 1 –  α confidence interval for the parameter, we reject H₀. For example, consider a two-tailed hypothesis test with α = 0.05and

H₀: μ = 21
H₁: μ ≠ 21

A random sample of size 33 has a sample mean x = 22 from a population with standard deviation σ = 3.

(a) What is the value of c = 1 − α?


Using the methods of Chapter 7, construct a 1 − α confidence interval for μ from the sample data. (Round your answers to two decimal places.)

What is the value of μ given in the null hypothesis (i.e., what is k)?
k =  

1.a). When do researchers use ANOVA vs. Chi-square test? Indicate two main characteristics of ANOVA and Chi-square tests (two for each test).

1.b). What are some of the major limitations of both ANOVA and Chi-square tests? (at least two for each)