A car company is attempting to develop a reasonably priced gasoline that will deliverimproved gasoline mileages. As part of its development process, the company would like to compare the effects of three types of gasoline (A, B and C) on gasoline mileage. For testing purposes, the company will compare the effects of gasoline types A, B and C on the gasoline mileage obtained by a popular mid-size car. 10 cars are randomly selected to be assigned toeach gasoline type (A, B and C), i.e.,nA =nB = nC = 10. The gasoline mileage for eachtest drive is measured.It is found that the gasoline mileage sample means of the three groups are 34.92, 36.56 and 33.98. The ANOVA table for the three-group model is summarized as following.

Let μA, μB, and μC be the mean mileages of gasoline types A, B, and, C respectively. Carry out an overal test to determine if there is significant difference among μA, μB, and μC at the sinificance level of 1%.

Do students perform the same when they take an exam alone as when they take an exam in a classroom setting? Eight students were given two tests of equal difficulty. They took one test in a solitary room and they took the other in a room filled with other students. The results are shown below.

Assume a Normal distribution. What can be concluded at the the αα = 0.01 level of significance level of significance?

For this study, we should use Select an answerz-test for a population proportionz-test for the difference between two population proportionst-test for the difference between two independent population meanst-test for a population meant-test for the difference between two dependent population means

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

H0:H0:  Select an answerμdμ1p1 ?=<>≠ Select an answer0μ2p2 (please enter a decimal)   

H1:H1:  Select an answerp1μdμ1 ?=><≠ Select an answer0μ2p2 (Please enter a decimal)

2. The test statistic ?tz = (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 answeracceptrejectfail to reject the null hypothesis.
6. Thus, the final conclusion is that ...
   • The results are statistically insignificant at αα = 0.01, so there is statistically significant evidence to conclude that the population mean test score taking the exam alone is equal to the population mean test score taking the exam in a classroom setting.
   • The results are statistically significant at αα = 0.01, so there is sufficient evidence to conclude that the eight students scored the same on average taking the exam alone compared to the classroom setting.
   • The results are statistically significant at αα = 0.01, so there is sufficient evidence to conclude that the population mean test score taking the exam alone is not the same as the population mean test score taking the exam in a classroom setting.
   • The results are statistically insignificant at αα = 0.01, so there is insufficient evidence to conclude that the population mean test score taking the exam alone is not the same as the population mean test score taking the exam in a classroom setting.

Open the files for the Course Project and the data set.

For each of the five variables, process, organize, present, and summarize the data. Analyze each variable by itself using graphical and numerical techniques of summarization. Use Excel as much as possible, explaining what the results reveal. Some of the following graphs may be helpful: stem-leaf diagram, frequency/relative frequency table, histogram, boxplot, dotplot, pie chart, and bar graph. Caution: not all of these are appropriate for each of these variables, nor are they all necessary. More is not necessarily better. In addition, be sure to find the appropriate measures of central tendency, the measures of dispersion, and the shapes of the distributions (for the quantitative variables) for the above data. Where appropriate, use the five number summary (the Min, Q1, Median, Q3, Max). Once again, use Excel as appropriate, and explain what the results mean. Analyze the connections or relationships between the variables. There are 10 possible pairings of two variables. Use graphical as well as numerical summary measures. Explain the results of the analysis. Be sure to consider all 10 pairings. Some variables show clear relationships, whereas others do not. Report Requirements From the variable analysis above, provide the analysis and interpretation for three individual variables. This would include no more than one graph for each, one or two measures of central tendency and variability (as appropriate), the shapes of the distributions for quantitative variables, and two or three sentences of interpretation. For the 10 pairings, identify and report only on three of the pairings, again using graphical and numerical summary (as appropriate), with interpretations. Please note that at least one pairing must include a qualitative variable, and at least one pairing must not include a qualitative variable. Prepare the report in Microsoft Word, integrating graphs and tables with text explanations and interpretations. Be sure to include graphical and numerical back up for the explanations and interpretations. Be selective in what is included in the report to meet the requirements of the report without extraneous information. All DeVry University policies are in effect, including the plagiarism policy. Project Part A report is due by the end of Week 2. Project Part A is worth 100 total points. See the grading rubric below. Submission: The report, including all relevant graphs and numerical analysis along with interpretations Format for report: Brief Introduction Discuss the first individual variable, using graphical, numerical summary and interpretation. Discuss the second individual variable, using graphical, numerical summary and interpretation. Discuss the third individual variable, using graphical, numerical summary and interpretation. Discuss the first pairing of variables, using graphical, numerical summary and interpretation. Discuss the second pairing of variables, using graphical, numerical summary and interpretation. Discuss the third pairing of variables, using graphical, numerical summary and interpretation. Conclusion

) The Paralyzed Veterans of America is a philanthropic organization that relies on contributions. They send free mailing labels and greeting cards to potential donors on their list and ask for a voluntary contribution. To test a new campaign, they recently sent letters to a random sample of 100,000 potential donors and received 4781 donations.

i. Give a 95% confidence interval for the true proportion of those from their entire mailing list who may donate. What is the margin of error of your confidence interval?

ii. Interpret your confidence interval. A staff member thinks that the true rate is 5%. Given the confidence interval you found, do you think that percentage plausible? Why?

iii. A confidence interval based on the same sample is (0.04676, 0.04886). What is the confidence level of this confidence interval?

if one card is drawn from an ordinary deck of card, find the probability of getting each event. a. a 7 or an 8 or a 9, b. a spade or a queen or a king, c. a club or a fade card, d. an ace or a diamond or a heart, e. a 9 or a 10 or a spade or a club

This problem is based on information taken from The Merck Manual (a reference manual used in most medical and nursing schools). Hypertension is defined as a blood pressure reading over 140 mm Hg systolic and/or over 90 mm Hg diastolic. Hypertension, if not corrected, can cause long-term health problems. In the college-age population (18-24 years), about 9.2% have hypertension. Suppose that a blood donor program is taking place in a college dormitory this week (final exams week). Before each student gives blood, the nurse takes a blood pressure reading. Of 200 donors, it is found that 28 have hypertension. Do these data indicate that the population proportion of students with hypertension during final exams week is higher than 9.2%? Use a 5% level of significance. (a) What is the level of significance? State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? H0: p = 0.092; H1: p < 0.092; left-tailed H0: p > 0.092; H1: p = 0.092; right-tailed H0: p = 0.092; H1: p ≠ 0.092; two-tailed H0: p = 0.092; H1: p > 0.092; right-tailed (b) What sampling distribution will you use? Do you think the sample size is sufficiently large? The Student's t, since np > 5 and nq > 5. The standard normal, since np < 5 and nq < 5. The standard normal, since np > 5 and nq > 5. The Student's t, since np < 5 and nq < 5. What is the value of the sample test statistic? (Round your answer to two decimal places.) (c) Find the P-value of the test statistic. (Round your answer to four decimal places.) Sketch the sampling distribution and show the area corresponding to the P-value. Maple Generated Plot Maple Generated Plot Maple Generated Plot Maple Generated Plot (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α? At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant. At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. (e) State your conclusion in the context of the application. There is sufficient evidence at the 0.05 level to conclude that the true proportion of students with hypertension during final exams week is higher than 0.092. There is insufficient evidence at the 0.05 level to conclude that the true proportion of students with hypertension during final exams week is higher than 0.092.

Crime concerns in China. A 2013 poll found that 24.2% of Chinese adults see crime as a very big problem, and the standard error for this estimate, which can reasonably be modeled using a normal distribution, is SE = 1.3%. Suppose an issue will get special attention from the Chinese government if more than 1-in-5 Chinese adults express concern on an issue.

1. Choose words from the dropdown choices to construct hypotheses regarding whether or not crime should receive special attention by the Chinese government according to the 1-in-5 guideline. Before making your choices consider the appropriateness of using a one-sided or two-sided test for this exercise. That is, for this decision process, would we care about one or both directions?

H0:H0: The proportion of adults in China who see crime as a very big problem is  ? more than not more than different from not different from less than not less than   ? 20% 24.2% 1.3% . The observed difference  ? is is not  due to chance.

HA:HA: The proportion of adults in China who see crime as a very big problem is  ? more than not more than different from not different from less than not less than   ? 20% 24.2% 1.3% . The observed difference  ? is is not  due to chance.

2. Calculate a z-score using the observed percentage and the two model parameters. Round to four decimal places. z =

3. Use the normal model to calculate a p-value. Round to four decimal places. p =

4. Based on your p-value, should crime receive special attention from the Chinese government?

? Yes No  because we  ? should should not  reject the null hypothesis.

Clint Barton is a self-employed consultant who runs his company, Hawkeye Solutions, out of a house that he owns that he does not live in. He uses the main floor for his work and rents out the second floor to a tenant. Since he uses a fair amount of computing in his work, he wants to make sure that he writes off a representative portion of the electrical bill for the house against the business. In the past, he estimated that 70% of the electricity in the house goes towards the business.

Since the Canada Revenue Agency might want to see documentation about his expenses, Barton wants to sample some of the power use to provide support for his case. Since the building has central heating and cooling, these electrical costs are shared evenly as utilities and Barton has already accounted for them separately.

Barton connected monitors to lines going to each floor for non-utility power. Because he has had disagreements about proper expenses in the past, he wants to provide strong evidence to the Canada Revenue Agency to support his claim that he uses 70% of the non-utility power for the business.

Design a test for Barton where he will record the values of the power going upstairs and to the main floor every day for a month (30 days). And answer the following questions (use complete sentences and exact equations where possible):

Barton does the test as you outline above. He finds over the course of the sample that the business used $320 of power and the upstairs used $80.

f) What is the value of the test statistic in this case?

g) What is the decision of the test in this case? Explain your reasoning.

h) What does this mean for Barton’s attempt to get sufficient documentation?

A month later, Barton does a test with a sample of 2 months (60 days). He finds over the course of the sample that the business used $720 of power and the upstairs used $180.

i) What is the value of the test statistic in this case?

j) What is the decision of the test in this case? Explain your reasoning.  

k) What does this mean for Barton’s attempt to get sufficient documentation?  

t-test data,

Calculate the pooled variance for this dataset.

Group 1= 9.7, 9.5, 9.2, 8.5, 10.9, 9.8, 8.7, 9.8, 7.9, 9.0, 10.5, 8.9, 10.0, 8.9, 6.8, 8.2, 9.3, 10.5, 8.5, 9.4

Group 2= 8.1, 7.8, 7.6, 8.1, 9.9, 8.6, 8.8, 9.1, 10.4, 9.1, 6.9, 7.3, 6.7, 5.5, 9.6, 7.8, 8.7, 9.5, 7.8, 8.2

An ANOVA test was conducted in R with the numbers...

monkey group 1= 9.7, 9.2, 9.5, 9.5, 10.9, 9.8, 8.7, 7.9, 9.8, 9, 10.5, 8.9, 10, 8.9, 6.8, 9.3, 8.2, 8.5, 9.4, 10.5

Monkey group 2= 8.1, 7.8, 7.6, 9.9, 8.1, 9.1, 8.8, 10.4, 8.6, 6.9, 9.1, 6.7, 7.3, 7.8, 9.6, 8.7, 5.5, 9.5, 8.2, 7.8

What value in the ANOVA output would be identical to the pooled variance found from the t-test data?

Show how to answer this in EXCEL ONLY, NO megastat or minitab, etc.. Please highlight what data tools or formulas were used.

A survey investigated the public’s attitude toward the federal deficit. Each sampled citizen was classified as to whether he or she felt the government should reduce the deficit or increase the deficit, or if the individual had no opinion. The sample results of the study by gender are reported to below.

At the .05 significance level, is it reasonable to conclude that gender is independent of a person’s position on the deficit?

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 60 home theater systems has a mean price of $111.00. Assume the population standard deviation is $16.20.

The 90% confidence interval is(--,--)

The 99% confidence interval is(--,--)

Which interval is wider?

. You measure 36 textbooks' weights, and find they have a mean weight of 30 ounces. Assume the population standard deviation is 10 ounces. Based on this, construct a 90% confidence interval for the true population mean textbook weight.

Give your answers as decimals, to two places

Assume that a sample is used to estimate a population proportion p. Find the 80% confidence interval for a sample of size 155 with 138 successes. Enter your answer using decimals (not percents) accurate to three decimal places.

You measure 48 turtles' weights, and find they have a mean weight of 57 ounces. Assume the population standard deviation is 13.8 ounces. Based on this, determine the point estimate and margin of error for a 95% confidence interval for the true population mean turtle weight.

Give your answers as decimals, to two places

Ask Your Teacher Recent studies have shown that about 20% of American adults fit the medical definition of being obese. A large medical clinic would like to estimate what percentage of their patients are obese, so they take a random sample of 100 patients and find that 16 are obese. Suppose that in truth, the same percentage holds for the patients of the medical clinic as for the general population, 20%. If the clinic took repeated random samples of 100 observations and found the sample proportion who were obese, into what interval should those sample proportions fall about 95% of the time? (Round your answers to two decimal places. Between _____ and _____

You wish to test the following claim at a significance level of α=0.02

      H0:μ=62.5
      H1:μ>62.5

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size 64 with mean 66.5 and a standard deviation of 12.7.

What is the test statistic for this sample? (Report answer accurate to 3 decimal places.)
test statistic =

What is the p-value for this sample? (Report answer accurate to 4 decimal places.)
p-value =

The number of men and women among professors in Math, Physics, Chemistry, Linguistics, and English departments from a SRS of small colleges were counted, and the results are shown in the table below.

Dept. Math Physics Chemistry Linguistics English

Men 16 . 36 12 10 14

Women 2 . 5 . 4 . 2 . 8

Test the claim that the gender of a professor is independent of the department. Use the significance level α=0.025

(a) The test statistic is χ2=

(b) The critical value is χ2=

(c) Is there sufficient evidence to warrant the rejection of the claim that the gender of a professor is independent of the department? A. No B. Yes