For Exercise 1 through 7, do a complete regression analysis by performing the following steps.

a.Draw the scatter plot.

b.Compute the value of the correlation coefficient.

c.Test the significance of the correlation coefficient at α = 0.01, using Table I or use the P-value method.

d.Determine the regression line equation if r is significant.

e.Plot the regression line on the scatter plot, if appropriate.

f.Predict y′ for a specific value of x, if appropriate.

3.Puppy Cuteness and Cost A researcher feels that a pet store bases the cost of puppies on the cuteness of the animals. Eight puppies were rated on their cuteness. The ratings were from 1 to 6, with 6 being the highest rating. The ratings and the cost in dollars of the puppies are shown. Is there a significant relationship between the variables? Please do by hand and show work.

Answer: 3.H₀: p = 0; H₁: ρ ≠ 0; r = 0.761; C.V. = ±0.834; d.f. = 6; do not reject. There is not a significant linear relationship between the rating and the cost. No regression analysis should be done. P = 0.0284

Recall that for a random variable to be a binomial random variable, you must have an experiment which meets the following three criteria:
1: There are exactly two outcomes for each trial.
2: There are a fixed number (n) of trials.
3: The trials are independent, and there is a fixed probability of success (p) and failure (q) for each trial.

For each of the two situations described below, please indicate if the variable X (as defined in each situation) can be considered a binomial random variable. If you think that X is a binomial variable, please explain how the situation specifically meets each of the three criteria, and identify the values of n and p. If you think X cannot be considered a binomial variable, please indicate which of the three criteria is/are not met (indicate all that apply), and provide a brief explanation for your choice(s). Hint: X can be considered a binomial random variable in only one of the two situations below, but I am not telling you which one, obviously.

Situation 1: A fair coin is tossed over and over again. Let X = the number of tosses until the third TAILS appears.

Situation 2: A box contains 10 marbles: 4 are red, 3 are white, and 3 are blue. A marble is randomly selected, returned to the box, then another marble is randomly selected. Let X = the number of red marbles selected in the two consecutive trials.

A consumer group conducted a study of SUV owners to estimate the mean highway mileage for their vehicles. A simple random sample of 91 SUV owners was selected, and the owners were asked to report their highway mileage. The following results were summarized from the sample data.

Sample Mean = 21.3 mpg

Standard Deviation = 6.3 mpg

Based on these sample data, compute and interpret a 90% confidence interval estimate for mean the highway mileage for SUVs.

The commercial for the new Meat Man Barbecue claims that it takes 20 minutes for assembly. A consumer advocate thinks that the assembly time is lower than 20 minutes. The advocate surveyed 11 randomly selected people who purchased the Meat Man Barbecue and found that their average time was 19.7 minutes. The standard deviation for this survey group was 2.1 minutes. What can be concluded at the the αα = 0.05 level of significance level of significance?

1. For this study, we should use Select an answert-test for a population meanz-test for a population proportion
2. The null and alternative hypotheses would be:

H0:H0:   ?pμ ?≠=<>   

H1:H1:   ?pμ ?<≠=>

3. The test statistic ?zt = (please show your answer to 3 decimal places.)
4. The p-value = (Please show your answer to 4 decimal places.)
5. The p-value is ?>≤ αα
6. Based on this, we should Select an answerfail to rejectrejectaccept the null hypothesis.
7. Thus, the final conclusion is that ...
   • The data suggest the populaton mean is significantly lower than 20 at αα = 0.05, so there is statistically significant evidence to conclude that the population mean amount of time to assemble the Meat Man barbecue is lower than 20.
   • The data suggest the population mean is not significantly lower than 20 at αα = 0.05, so there is statistically insignificant evidence to conclude that the population mean amount of time to assemble the Meat Man barbecue is equal to 20.
   • The data suggest that the population mean amount of time to assemble the Meat Man barbecue is not significantly lower than 20 at αα = 0.05, so there is statistically insignificant evidence to conclude that the population mean amount of time to assemble the Meat Man barbecue is lower than 20.

6. Paired annual rates of return data are collected from 8 randomly selected investment funds before and after The Federal Reserve cuts down interest rates. The dataset and relevant summery results are given in the table below. Suppose you are a financial analyst interested in finding out whether investment funds’ mean rate of return is significantly different before and after the interest rate adjustment.

The ALTURNATIVE hypothesis of this test is ________________________________________.

The significance level for this test should be chosen to be _______________________.

The numerical formula calculating test statistic is __________________________________________.

The test statistic is calculated to be_________________________.

The p-value is ___________________________.

Based on the p-value we _________________, (accept or reject H0)

In New York State, savings banks are permitted to sell a form of life insurance called savings bank life insurance (SBLI). The approval process consists of underwriting, which includes a review of the application, a medical information bureau check, possible requests for additional medical information and medical exams, and a policy compilation stage in which the policy pages are generated and sent to the bank for delivery. The ability to deliver approved policies to customers in a timely manner is critical to the profitability of this service to the bank. During a period of one month, a random sample of 27 approved policies was selected, and the total processing time, in days, was as shown below and stored in the file INSURANCE:

73 19 16 64 28 28 31 90 60 56 31 56 22 18

45 48 17 17 17 91 92 63 50 51 69 16 17

a. Construct and interpret a 95% confidence interval estimate of the population mean processing time. Use Minitab. (Don't worry about this one.)

b. What assumption must you make about the population distribution in order to construct the confidence interval in (a)?

c. Do you think that the assumption needed in order to construct the confidence interval estimate in (a) is valid? Explain.

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?