How do horsepower and weight affect the mileage of family cars? Data from a sample of 12 2012 family cars are given below (Data extracted from “Top 2012 Cars,” Consumer Reports, April 2012, pp. 40–73.) Develop a regression model to predict mileage (as measured by miles per gallon) based on the horsepower of the car’s engine and the weight of the car (in pounds). Car MPG Horsepower Weight Audi A3 25 200 3305 Chrysler 200 21 173 3590 Dodge Avenger 21 173 3440 Ford Fusion 24 240 3365 Honda Accord 25 177 3285 Kia Optima 25 200 3260 Mazda6 24 170 3185 Mitsubishi Galant 23 160 3430 Nissan Altima 26 175 3155 Suburu Legacy 25 170 3390 Toyota Camry 27 173 3155 Volkswagen Passat 25 170 3270 Use Excel to find the multiple regression results for this problem. Include Excel results with your submission. a. State the multiple regression equation for this problem. b. Interpret the meaning of the slopes, b1 and b2, in this problem. c. Does the regression coefficient, b0, has a practical meaning in the context of this problem. d. Predict the miles per gallon for cars that have 190 horsepower and weigh 3,500 pounds. e. Compute the coefficient of multiple determination, r2, and interpret its meaning. f. Compute the adjusted r2.

Use the normal distribution to find a confidence interval for a proportion p given the relevant sample results. Give the best point estimate for p, the margin of error, and the confidence interval. Assume the results come from a random sample. A 95% confidence interval for p given that p Overscript ^ EndScripts equals 0.42 and n equals 450. Round your answer for the best point estimate to two decimal places, and your answers for the margin of error and the confidence interval to three decimal places.

best point estimate ?

MOE?

95% CI?

Let μ1 denote true average tread life for a premium brand of P205/65R15 radial tire, and let μ2 denote the true average tread life for an economy brand of the same size. Test H0: μ1 − μ2 = 5000 versus Ha: μ1 − μ2 > 5000 at level 0.01, using the following data: m = 35, x = 42,100, s1 = 2500, n = 35, y = 36,900, and s2 = 1500. Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) z = 0.4058 Correct: Your answer is correct. P-value = 0.5942 Incorrect: Your answer is incorrect.

11. For a local basketball league, there were 10 teams whose players were assigned to a team based on their score on an abilities test. Those results are given below.

The summary statistics are:

1. From just looking at the summary data, what conclusions might you draw? (You may want to talk about average and/or variance)

During the holiday season, shoppers were asked to estimate how much money they spent on gifts for themselves. Raw data is given below. Are the reported amounts significantly less than the actual amounts as determined from the receipts?

1) Write Ho (null) and H1 (alternative); indicate which is being tested.

2) Perform the statistical test ad write answer to the original question as a statement related to the original query

2) Construct a 99% confidence interval estimate of the mean difference between reported amounts and actual amounts . Interpret the resulting confidence interval, does it contain 0?

A student in a statistics class tossed a die 300 times and obtained the results shown in the table. Is the die fair? In other words does it fit a uniform distribution? Let alpha =.05        

A. What is the null hypothesis?

B. What is the alternative hypothesis?

C. What distribution are you using?

D. What test are you running?

E. What is your conclusion?

You spoke with your instructor and she claimed that the average number of hours that you should study has to be more than 5 hours per week which will help you achieve an above average grade on any subject. She also suggested as a practice that you can test her claim and let her know what your conclusion is. So you decided to contact your peers and gather information to conduct a hypothesis to test your instructors claim.

Questions:

1. Contact at least 15 peers (they don’t have to be from the same class) and obtain how much time they study each week.

2. If you are to conduct a hypothesis test using the data you gathered,
   1. Which test (t test or z test) do you think be appropriate and why?
      (Hint: think about whether you have the population or sample standard deviation available)

2. Is this a test on population proportion or mean?

3. Calculate the sample statistics (sample mean or sample proportion based on the information given) (1 mark)

4. Use the data set you gathered to conduct a hypothesis test to determine your instructor’s claim. Use 0.05 level of significance. Please show your work, the 5 steps as described in the textbook.

3. Construct a 95% confidence interval for the population mean number of hours. Show your work.

When is SRS preferred over stratified sampling? That is, under what circumstances is straified sampling inferior to SRS? My professor said "when within variance is larger, and between mean is smaller" stratified sampling isnt going to do much, and SRS would suffice. However, it is unclear what this means. Thoughts?

A sample of 200 science professor annual salaries yielded a mean value of $60,000. If the variance of population salary is $225 million, answer the following questions at 99% confidence The Point Estimate is ..... The Standard error is ..... The Margin of Error is ..... The Critical Statistic is ...... The population mean is estimated to range from .......... to ........ in ...........% of the time

1. The following data were obtained from a two-factor independent-measures experiment with n

= 5 participants in each treatment condition.

B1                       B2                         B3

1. State the hypotheses for each of the three separate tests included in the two-factor ANOVA.
2. Calculate degrees of freedom and locate the critical region for each of the three tests.
3. Calculate the three F-ratios.
4. State a conclusion for each test (Alpha level = .05).

Let P_Sand P_Drepresent the prices charged for each standard golf bag and deluxe golf bag respectively. Assume that “S” and “D” are demands for standard and deluxe bags respectively.

S = 2250 – 15P_S                                                                                                                                                                    (8.1)

D = 1500 – 5P_D                                                                                                                                                                      (8.2)

Revenue generated from the sale of S number of standard bags is P_S*S. Cost per unit production is $70 and the cost for producing S number of standard bags is 70*S.

So the profit for producing and selling S number of standard bags = revenue – cost = P_SS – 70S                            (8.3)

By rearranging 8.1 we get                                  

15P_S= 2250 – S or

                                    P_S= 2250/15 – S/15 or

                                    P_S= 150 – S/15                                                                                                                                                                     (8.3a)

Substituting the value of P_Sfrom 8.3a in 8.3 we get the profit contribution of the standard bag:

                                    (150 –S/15)S – 70S = 150S – S²/15 – 70S = 80S – S²/15                                                                                 (8.4)

Revenue generated from the sale of D number of deluxe bags is P_D*D. Cost per unit production is $150 and the cost for producing D number of deluxe bags is 150*D.

So the profit for producing and selling D number of deluxe bags = revenue – cost = P_DD – 150D                           (8.4a)

By rearranging 8.2 we get                                  

5P_D= 1500 – D or

                                    P_D= 1500/5 – D/5 or

                                    P_D= 300 – D/5                                                                                                                                                                       (8.4b)

Substituting the value of P_Dfrom 8.4b in 8.4a we get the profit contribution of the deluxe bags:

                                    (300 -D/5)D – 150D = 300D – D²/5 – 150D = 150D – D²/5                                                                          (8.4c)

By adding 8.4 and 8.4c we get the total profit contribution for selling S standard bags and D deluxe bags.

                                    Total profit contribution = 80S –S²/15 + 150D – D²/5                                                                                 (8.5)

Homework assignment:

Reconstruct new objective function for 8.5 by changing “15P_S” to “8P_S” in 8.1, “5P_D” to “10P_D” in 8.2, cost per unit standard bagfrom 70 to 91 and cost per unit deluxe bag from 150 to 125. Keep other parameter values unchanged. Use up to 2 decimal points accuracy. Substitute the new expression for 8.5 in the excel solver workbook as explained in the class and solve for the optimal combination values for S and D..Instructor will not accept any homework late or submitted outside the class. Make sure you submit the results (just one page excel printout). Write/type your full name (first name first) in upper case, last 4 of your student ID, and, your new objective function expression (like equation 8.5 above) on the printout. Use S and D instead of b15 or c15 in the formulation. If you fail to follow the instructions, you will lose points.

*PLEASE Show also Excel Solution*

Determine the following z-scores: a. z0.1 = __________ b. z0.025 = __________

I don't understand the answer which has been posted. Thanks.

PART 2:

The researchers hypothesized that mice consuming more saturated fats will have a higher probability of becoming obese and developing symptoms of diabetes. To test for dietary effects on the development of metabolic disease, the researchers collected additional data from the two cohorts of mice. They measured the fasting blood glucose levels and they performed an insulin tolerance test (effect of a dose of insulin on blood glucose level). Data are reported as means (±SEM).

• Using a t-test, determine whether the difference in the fasting blood glucose levels for the lard-fed and the fish oil-fed mice is significant.

• Plot the glucose over time data.

• Did the two groups of mice differ in their response to the same dose of insulin? At which time points?

• What conclusions can you make about the effect of the type of dietary fat on carbohydrate metabolism?

PART 3:

To determine whether the difference in the microbiota is responsible for the difference in the weight gain or just a consequence of the different diet, the researchers raised mice for 11 weeks on either a lard or fish-oil diet. Then they took two new groups of mice and treated them with antibiotic to kill their gut microbiota. These mice then received transplants of the microbiota from the mice that had been fed either lard or fish oil for 11 weeks. All of the “transplanted” mice were maintained on a lard diet for 3 weeks to see if there was a difference in their weight gain.

• Was there a significant difference in the weight gain in these two groups of mice?

• What conclusion can you make about the effect of the microbiota composition versus the diet on weight gain?

• What additional information would you want to have to support your conclusion?

A survey found that 62​% of callers complain about the service they receive from a call center. State the assumptions and determine the probability of each event described below.

​(a) The next three consecutive callers complain about the service.

​(b) The next two callers​ complain, but not the third.

​(c) Two out of the next three calls produce a complaint.

​(d) None of the next 10 calls produces a complaint.

The probability that the next three callers complain is about?

Most vertebrates have testosterone, and have behaviors that are mediated by this hormone. Testosterone can be helpful to animals, by enhancing (e.g.) territory acquisition, or harmful, by (e.g.) causing physiological stress. When male blackbirds are exposed to other male blackbirds, their testosterone levels change. In order to understand the impacts of testosterone on male blackbirds, researchers followed a few individual males, to monitor testosterone changes after encountering another male.   A pre-exposure measurement was made (in nanograms/deciliter) and a post-exposure measurement was taken, data below. Researchers will test the hypothesis that pre-exposure testosterone levels are the same as post-testosterone levels.

(2 points) 1. Does this hypothesis test depend on a t distribution, a Z distribution, or a χ² distribution?

(2 points) 2. What are the df for the test you will do?

(2 points) 3a. Is this a one-tailed, or a two-tailed test?

(2 points) 3b. How would you rephrase the hypothesis test to make it the other way (for instance, if you chose a one-tailed test in 3a, how would you re-phrase my original question to make it a two-tailed test?)

(2 points) 4. What is the hypothesized difference?

(2 points) 5. Calculate your test statistic here:

(2 points) 6. Do you reject or fail to reject the null hypothesis?

(2 points) 7. How would you articulate your conclusion to my grandmother, who would not like to hear about rejecting (or failing to reject) null hypotheses, but would be interested to know about blackbirds?

!!!!!!ANSWER ALL!!!!