1. The standard recommendation for automobile oil changes is once every 5000 miles. A local mechanic is interested in determining whether people who drive more expensive cars are more likely to follow the recommendation. Independent random samples of 45 customers who drive luxury cars and 40 customers who drive compact lower-price cars were selected. The average distance driven between oil changes was 5187 miles for the luxury car owners and 5389 miles for the compact lower-price car owners. The sample standard deviations were 424 and 507 miles for the luxury and compact groups, respectively. Assume that the two population distributions of the distances between oil changes have the same standard deviation. You would like to test if the mean distance between oil changes is less for all luxury cars than that for all compact lower-price cars.

Let μ₁ denote the mean distance between oil changes for luxury cars, and μ₂ denote the mean distance between oil changes for compact lower-price cars. Calculate the appropriate statistic for this test. Round your intermediate calculations (all standard deviations) as well as your final answer to the nearest hundredth.

2. A local college cafeteria has a self-service soft ice cream machine. The cafeteria provides bowls that can hold up to 16 ounces of ice cream. The food service manager is interested in comparing the average amount of ice cream dispensed by male students to the average amount dispensed by female students. A measurement device was placed on the ice cream machine to determine the amounts dispensed. Random samples of 85 male and 78 female students who got ice cream were selected. The sample averages were 7.23 and 6.49 ounces for the male and female students, respectively. Assume that the population standard deviations are 1.22 and 1.17 ounces, respectively. You would like to test whether the average amount of ice cream dispensed by all make college students is different from the average amount dispensed by all female college students.

a. Let μ1 denote the average amount of ice cream dispensed by all male college students, and μ2 denote the average amount of ice cream dispensed by all female college students. Calculate an appropriate test statistic for this case. Round your intermediate calculations to the nearest ten thousandth and round your final answer to the nearest hundredth.

b. Let μ1 denote the average amount of ice cream dispensed by all male college students, and μ2 denote the average amount of ice cream dispensed by all female college students. Suppose the test statistic associated to this test is 3.95. Calculate the p-value. Round your answer to the nearest ten thousandth (e.g., 0.1234).

The port of South Louisiana, located along 54 miles of the Mississippi River between New Orleans and Baton Rouge, is the largest bulk cargo port in the world. The U.S. Army Corps of Engineers reports that the port handles a mean of 4.5 million tons of cargo per week (USA Today, September 25, 2012). Assume that the number of tons of cargo handled per week is normally distributed with a standard deviation of .82 million tons.

a. What is the probability that the port handles less than 5 million tons of cargo per week (to 4 decimals)?

b. What is the probability that the port handles 3 or more million tons of cargo per week (to 4 decimals)?

c. What is the probability that the port handles between 3 million and 4 million tons of cargo per week (to 4 decimals)?

d. Assume that 85% of the time the port can handle the weekly cargo volume without extending operating hours. What is the number of tons of cargo per week that will require the port to extend its operating hours (to 2 decimals)?

1. A manager wishes to check the miles her taxi cabs are driven each day. Her findings are shown below. Construct a frequency distribution, using ten classes.

   136	97	163	118	146	109	99
   124	119	151	122	131	124	101
   118	118	119	142	124	137	106
   152	99	107	151	139	116	137
   143	105	99	125	108	160	142

   What is the Range? Blank 1

   What is the Class Width? Blank 2

   Fill in the table after creating it on paper. rf and crf are rounded to two decimal places. To input the Class Limits and Class Boundaries, you will need to put the lower class limit/boundary in the first blank and the upper class limit/boundary in the blank below where you input the lower. It is the way the Blackboard tool works.

   Class Limits	Class Boundaries	Midpoints	f	cf	rf	crf
   Blank 3-Blank 4	Blank 5-Blank 6	Blank 7	Blank 8	Blank 9	Blank 10	Blank 11
   Blank 12-Blank 13	Blank 14-Blank 15	Blank 16	Blank 17	Blank 18	Blank 19	Blank 20
   Blank 21-Blank 22	Blank 23-Blank 24	Blank 25	Blank 26	Blank 27	Blank 28	Blank 29
   Blank 30-Blank 31	Blank 32-Blank 33	Blank 34	Blank 35	Blank 36	Blank 37	Blank 38
   Blank 39-Blank 40	Blank 41-Blank 42	Blank 43	Blank 44	Blank 45	Blank 46	Blank 47
   Blank 48-Blank 49	Blank 50-Blank 51	Blank 52	Blank 53	Blank 54	Blank 55	Blank 56
   Blank 57-Blank 58	Blank 59-Blank 60	Blank 61	Blank 62	Blank 63	Blank 64	Blank 65
   Blank 66-Blank 67	Blank 68-Blank 69	Blank 70	Blank 71	Blank 72	Blank 73	Blank 74
   Blank 75-Blank 76	Blank 77-Blank 78	Blank 79	Blank 80	Blank 81	Blank 82	Blank 83
   Blank 84-Blank 85	Blank 86-Blank 87	Blank 88	Blank 89	Blank 90	Blank 91	Blank 92

Ex 7. Michael and Greg share an apartment 10 miles from campus. Michael thinks that the fastest way to get to campus is to drive the shortest route, which involves taking several side streets. Greg thinks the fastest way is to take the route with the highest speed limits, which involves taking the highway most of the way but is two miles longer than Michael’s route. You recruit 50 college friends who are willing to take either route and time themselves. After compiling all the results, you found that the travel time for Michael’s route follows a Normal distribution with a mean equal to 30 minutes and a standard deviation equal to 5 minutes. Greg’s route follows a Normal distribution with a mean equal to 26 minutes and a standard deviation of 9.5 minutes. 1)Which route is faster and why? 2)Which route is more reliable and why? 3) Suppose that you leaving home headed for a University exam. Obviously, you don’t want to be late. You are leaving home at 5:15 and the exam is at 6:00 PM. Which route would you take to avoid being late and why? Show your calculations.

Michael and Greg share an apartment 10 miles from campus. Michael thinks that the fastest way to get to campus is to drive the shortest route, which involves taking several side streets. Greg thinks the fastest way is to take the route with the highest speed limits, which involves taking the highway most of the way but is two miles longer than Michael’s route. You recruit 50 college friends who are willing to take either route and time themselves. After compiling all the results, you found that the travel time for Michael’s route follows a Normal distribution with mean equal to 30 minutes and standard deviation equal to 5 minutes. Greg’s route follows a Normal distribution with a mean equal to 26 minutes and a standard deviation of 9.5 minutes.

1)Which route is faster and why?

2)Which route is more reliable and why?

3) Suppose that you leaving home headed for a University exam. Obviously, you don’t want to be late. You are leaving home at 5:15 and the exam is at 6:00PM. Which route would you take to avoid being late and why? Show your calculations.

Question 4

Researchers studied four different blends of gasoline to determine their effect on miles per gallon (MPG) of a car. An experiment was conducted with a total of 28 cars of the same type, model, and engine size, with 7 cars randomly assigned to each treatment group. The gasoline blends are referred to as A,B,C, and D.The MPGs are shown below in the table

Gasoline Miles Per

Blend Gallon

A 26 28 29 23 24 25 26

B 27 29 31 32 25 24 28

C 29 31 32 34 24 28 27

D 30 31 37 38 36 35 29

We want to test the null hypothesis that the four treatment groups have the same mean MPG vs. the alternative hypothesis that not all of the means are equal.

a) Before carrying out the analysis, check the validity of any assumptions necessary for the analysis you will be doing. Write a brief statement of your findings

b) Test the null hypothesis that the four gasoline blends have the same mean MPGs, i.e., Test Ho: ua=ub=uc=ud vs. the alternative hypothesis Ha: not all the means are equal.

c) If your hypothesis test in (b) indicates a significant difference among the treatment groups, conduct pairwise multiple comparison tests on the treatment group means. Underline groups of homogeneous means.

d) Briefly state your conclusions.

( Use IBM SPSS for all calculations)

The Bahamas is a tropical paradise made up of 700 islands sprinkled over 100,000 square miles of the Atlantic Ocean. According to the figures released by the government of the Bahamas, the mean household income in the Bahamas is $34,803 and the median income is $31,729. A demographer decides to use the lognormal random variable to model this nonsymmetric income distribution. Let Y represent household income, where for a normally distributed X, Y = e^X. In addition, suppose the standard deviation of household income is $13,000. Use this information to answer the following questions. [You may find it useful to reference the z table.]

a. Compute the mean and the standard deviation of X. (Round your intermediate calculations to at least 4 decimal places and final answers to 4 decimal places.)

b. What proportion of the people in the Bahamas have household income above the mean? (Round your intermediate calculations to at least 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.)

c. What proportion of the people in the Bahamas have household income below $21,000? (Round your intermediate calculations to at least 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.)

d. Compute the 65th percentile of the income distribution in the Bahamas. (Round your intermediate calculations to at least 4 decimal places, “z” value to 3 decimal places, and final answer to the nearest whole number.)

-When first observed, an oil spill covers 8 square miles. Measurements show that the area is tripling every 6 hrs. Find an exponential model for the area A (in mi²) of the oil spill as a function of time t (in hr) from the beginning of the spill. (Enter a mathematical expression.)

A(t)=

-An internet analytics company measured the number of people watching a video posted on a social media platform. The company found 129 people had watched the video and that the number of people who had watched it was increasing by 30% every 3 hours.

A=

-A restaurant owner deposits $6,000 into an account that earns an annual interest rate of 6% compounded monthly. Find an exponential growth model for A, the value of the account (in dollars) after t years. (Enter a mathematical expression)

A=

**please show work

Miles Hardware has an annual cash dividend policy that raises the dividend each year by 12​%. Last​ year's dividend, Div0​, was $1.70 per share. Investors want a return of 16​% on this stock. What is the​ stock's price if

a.the company will be in business for 10 years and not have a liquidating​ dividend?

b.the company will be in business for 20 years and not have a liquidating​ dividend?

c.the company will be in business for 25 years and not have a liquidating​ dividend?

d. the company will be in business for 40 years and not have a liquidating​ dividend?

e.the company will be in business for 90 years and not have a liquidating​ dividend?

f.the company will be in business​ forever?

Question 4 Researchers studied four different blends of gasoline to determine their effect on miles per gallon (MPG) of a car. An experiment was conducted with a total of 28 cars of the same type, model, and engine size, with 7 cars randomly assigned to each treatment group. The gasoline blends are referred to as A,B,C, and D.The MPGs are shown below in the table Gasoline Miles Per Blend Gallon A 26 28 29 23 24 25 26 B 27 29 31 32 25 24 28 C 29 31 32 34 24 28 27 D 30 31 37 38 36 35 29 We want to test the null hypothesis that the four treatment groups have the same mean MPG vs. the alternative hypothesis that not all of the means are equal. a) Before carrying out the analysis, check the validity of any assumptions necessary for the analysis you will be doing. Write a brief statement of your findings b) Test the null hypothesis that the four gasoline blends have the same mean MPGs, i.e., Test Ho: ua=ub=uc=ud vs. the alternative hypothesis Ha: not all the means are equal. c) If your hypothesis test in (b) indicates a significant difference among the treatment groups, conduct pairwise multiple comparison tests on the treatment group means. Underline groups of homogeneous means. d) Briefly state your conclusions. ( Use IBM SPSS for all calculations)