An American consumer organization is currently examining the relationship among several variables including gasoline mileage as measured by miles per gallon; the horsepower of the car’s engine and the weight of the car (in pounds). A sample of 50 recent car models was selected and the results recorded. (provided in auto.xlxs) (a) Using the sample data attached, calculate the sample mean and standard deviation for the variables: - 1. Miles per gallon (MPG) 2. Horsepower 3. Weight (in pounds) (b) Is there any evidence of skewness in the data sets? Which data set displays greatest skewness? (c) Using the sample data on MPG, calculate the sample proportion of vehicles whose fuel economy exceeds 37 mpg and its corresponding standard deviation. (d) Indicate all possible relationship between the variables and comment on it. (You may use scatter diagram or Karl Pearson’s correlation coefficient) (e) Using the complete data set and using simple ordinary least squares regression formulae develop two models to explain the behavior of gasoline mileage (Miles per gallon) as a function of their- (i) Horsepower (ii) Weight f. Which model best describes the behavior of gasoline mileage? Explain your reasons here.

MPG   Horsepower   Weight
43.1   48   1985
19.9   110   3365
19.2   105   3535
17.7   165   3445
18.1   139   3205
20.3   103   2830
21.5   115   3245
16.9   155   4360
15.5   142   4054
18.5   150   3940
27.2   71   3190
41.5   76   2144
46.6   65   2110
23.7   100   2420
27.2   84   2490
39.1   58   1755
28   88   2605
24   92   2865
20.2   139   3570
20.5   95   3155
28   90   2678
34.7   63   2215
36.1   66   1800
35.7   80   1915
20.2   85   2965
23.9   90   3420
29.9   65   2380
30.4   67   3250
36   74   1980
22.6   110   2800
36.4   67   2950
27.5   95   2560
33.7   75   2210
44.6   67   1850
32.9   100   2615
38   67   1965
24.2   120   2930
38.1   60   1968
39.4   70   2070
25.4   116   2900
31.3   75   2542
34.1   68   1985
34   88   2395
31   82   2720
27.4   80   2670
22.3   88   2890
28   79   2625
17.6   85   3465
34.4   65   3465
20.6   105   3380

Bardi Trucking Co., located in Cleveland, Ohio, makes deliveries in the Great Lakes region, the Southeast, and the Northeast. Jim Bardi, the president, is studying the relationship between the distance a shipment must travel and the length of time, in days, it takes the shipment to arrive at its destination. To investigate, Mr. Bardi selected a random sample of 20 shipments made last month. Shipping distance is the independent variable and shipping time is the dependent variable. The results are as follows:

1. Draw a scatter diagram. Based on these data, does it appear that there is a relationship between how many miles a shipment has to go and the time it takes to arrive at its destination?

1. On the graph below, use the point tool to plot the point corresponding to the first Distance and its Shipping Time (Distance 1).

2. Repeat the process for the remainder of the sample (Distance 2, Distance 3, … ).

3. To enter exact coordinates, double-click on the point and enter the exact coordinates of x and y.

4. b-1. Fill in the blanks. (Round your answers to 3 decimal places. Negative values should be indicated by minus sign.)

1. b-2. State the decision rule for 0.02 significance level: H₀: ρ ≤ 0; H₁: ρ > 0. (Round your answer to 3 decimal places.)

2. b-3. Compute the value of the test statistic. (Negative value should be indicated by a minus sign. Round your answer to 3 decimal places.

3. b-4. Can we conclude that there is a positive correlation between distance and time? Use the 0.02 significance level.

4. c-1. Determine the coefficient of determination. (Round your answer to 3 decimal places.)

5. c-2. Fill in the blank below. (Round your answer to 1 decimal place.)

6. Determine the standard error of estimate. (Round your answer to 3 decimal places.)

7. Would you recommend using the regression equation to predict shipping time?

• Yes

• No

17. A tire manufacturer claims that the average life of a certain grade of tire is 50,000 miles or more when used under normal driving conditions. A random sample of 20 tires is selected and tested and the sample mean is 49,650 miles. Assume the population of the lives is to be normal with standard deviation of 5,000 miles. At the 5% significance level, the manufacturer’s claim is tested. What is the decision rule in this test?

A. Reject H₀ if Z_STAT > +1.96; otherwise, do not reject H₀.

B. Reject H₀ if Z_STAT < –1.645; otherwise, do not reject H₀.

C. Reject H₀ if t_STAT > –1.7291; otherwise, do not reject H₀.

D. Reject H₀ if t_STAT < –2.0930 or t_STAT > +2.0930; otherwise, do not reject H₀.

18. The manager of a gasoline supply corporation wants to estimate the actual amount of gasoline contained in standard 42-gallon barrels purchased from a nationally known manufacturer. The manufacturer’s specifications state that the amount of gasoline is normally distributed with a standard deviation of 0.65 gallon. A random sample of 25 barrels is selected, and the sample mean amount of gasoline per 42-gallon barrel is 42.15 gallons. Construct a 90% confidence interval estimate for the population mean amount of gasoline contained in a standard 42-gallon barrel.

A. 42.15 ± 1.7109 (0.65) / 25

B. 42 ± 1.645 (0.65) / 5

C. 42 ± 1.7109 (0.65) / 25

D. 42.15 ± 1.645 (0.65) / 5

19. “Is live lecture over Zoom an effective way to conduct online lectures?” A pilot sample of 50 students of UM reveals that 18 of them gave a positive response. If a researcher wants to estimate the proportion of positive responses from all the students of UM, what should be the minimum sample size used if she wants the width of a 95% confidence interval estimate to be 0.10?

A. 355

B. 97

C. 385

D. 89

20. A dean of a business school is interested in determining whether the mean grade point average (GPA) of students is less than3.04. The population standard deviation is 0.41 A random sample of 200 students indicates a sample mean GPA of 2.94. A test is conducted at the 0.05 level of significance to determine whether the mean grade point average (GPA) of students is less than 3.04. What is the test statistic value in this test?

A. +0.244

B. –3.449

C. –0.244

D. +3.449

21.A random sample of 40 bags of flour is weighed. It is found that the sample mean is 453.08 grams. All weights of the bags of flour have a population standard deviation of 5.42 grams. What is the lower limit of an 80% confidence interval for the population mean weight?

A. 452.405 grams

B. 452.360 grams

C. 451.983 grams

D. No solution

Bardi Trucking Co., located in Cleveland, Ohio, makes deliveries in the Great Lakes region, the Southeast, and the Northeast. Jim Bardi, the president, is studying the relationship between the distance a shipment must travel and the length of time, in days, it takes the shipment to arrive at its destination. To investigate, Mr. Bardi selected a random sample of 20 shipments made last month. Shipping distance is the independent variable and shipping time is the dependent variable. The results are as follows:

Click here for the Excel Data File

1. Draw a scatter diagram. Based on these data, does it appear that there is a relationship between how many miles a shipment has to go and the time it takes to arrive at its destination?

1. On the graph below, use the point tool to plot the point corresponding to the first Distance and its Shipping Time (Distance 1).

2. Repeat the process for the remainder of the sample (Distance 2, Distance 3, … ).

3. To enter exact coordinates, double-click on the point and enter the exact coordinates of x and y.

1. b-1. Fill in the blanks. (Round your answers to 3 decimal places. Negative values should be indicated by minus sign.)

1. b-2. State the decision rule for 0.05 significance level: H₀: ρ ≤ 0; H₁: ρ > 0. (Round your answer to 3 decimal places.)

1. b-3. Compute the value of the test statistic. (Negative value should be indicated by a minus sign. Round your answer to 3 decimal places.)

1. b-4. Can we conclude that there is a positive correlation between distance and time? Use the 0.05 significance level.

1. c-1. Determine the coefficient of determination. (Round your answer to 3 decimal places.)

1. c-2. Fill in the blank below. (Round your answer to 1 decimal place.)

4. Determine the standard error of estimate. (Round your answer to 3 decimal places.)

5. Would you recommend using the regression equation to predict shipping time?

1. Find the​ (a) mean,​ (b) median,​ (c) mode, and​ (d) midrange for the given sample data.

An experiment was conducted to determine whether a deficiency of carbon dioxide in the soil affects the phenotype of peas. Listed below are the phenotype codes where 1=smooth-yellow​,2=smooth-green​, 3=wrinkled-yellow​, and 4=wrinkled-green.

Do the results make​ sense?

​(a) The mean phenotype code is _____.

2. Statistics are sometimes used to compare or identify authors of different works. The lengths of the first 10 words in a book by Terry are listed with the first 10 words in a book by David. Find the mean and median for each of the two​ samples, then compare the two sets of results.

The mean number of letters per word in​ Terry's book is _____.

3. Refer to the data set of​ times, in​ minutes, required for an airplane to taxi out for​ takeoff, listed below. Find the mean and median. How is it helpful to find the​ mean?

Click the icon for the taxi out takeoff data.

Find the mean and median of the data set using a calculator or similar data analysis technology.

The mean of the data set is _____ minutes.

4. Find the mean of the data summarized in the given frequency distribution. Compare the computed mean to the actual mean of 50.4 miles per hour.

The mean of the frequency distribution is _____ miles per hour.

5.Six different​ second-year medical students at Bellevue Hospital measured the blood pressure of the same person. The systolic readings​ (in mmHg) are listed below. Find the​ range, variance, and standard deviation for the given sample data. If the​ subject's blood pressure remains constant and the medical students correctly apply the same measurement​ technique, what should be the value of the standard​ deviation?

126   126   138   125   137   134

Range= ______ mmHg

Using Java,

1. Ask for the runner’s name

2. Ask the runner to enter a floating point number for the number of miles ran, like 3.6 or 9.5

3. Then ask for the number of hours, minutes, and seconds it took to run

4. Format the numbers with leading 0's if the pace is 8 minutes and 3 second, it should be 8:03 and for marathon time, if its 1 hour and 15 minutes and 9 seconds, it should be 1:15:09

5. Please read through the whole thing, as the pace table example and fastest man time is listed below...

• A marathon is 26.219 miles

• Pace is how long it takes in minutes and seconds to run 1 mile.
  

Example Input:
What is your first name? // user enters Pheidippides
How far did you run today? 10.6 // user enters 10.6 miles

How long did it take? Hours: 1 // user enters 1 hours

Minutes: 34 // user enters 34 minutes

Seconds: 17 // user enters 17 seconds

Example Output:

Hi Pheidippides
Your pace is 8:53 (minutes: seconds)
At this rate your marathon time would be 3:53:12
Good luck with your training!

After your program tells the user what their pace is, your program will build a table showing the following columns. The pace table should start with the fastest man time which is Eliud Kipchoge with a pace of 4:37 and 2:01:04 and continue in 17 minute and 37 second intervals until you reach the marathon time of the user.

Example: (THE PACE TABLE EXAMPLE)

Pace Table
Pace Marathon
4:37 2:01:04 ←- Eliud Kipchoge
5:17 2:18:41
5:57 2:36:18
6:37 2:53:55
7:18 3:11:32
7:58 3:29:09
8:38 3:46:46
8:53 3:53:12 ← Pheidippides

HINTS

• The table should start with the World Record pace and time which is 4:37, 2:01:04.

• Then continues in 17 minute and 37 second intervals until you reach the marathon time of the user.

• Use a static function to print the pace table, introduce a while loop.

• For the first person it should call a printTable function

  • Example : printTable (pace, “<--- Eliud Kipchoge”)

  • The pace table continues until it reaches the user

  • printTable (myPace, name) something like that  

• For the marathon and pace time, make sure the format has 0’s if the time is 9 seconds, it should be 09.

• Use the printf statement for formatting output (“02d %f%s”)

The Park Manager at Fort Fisher State Park in North Carolina believes the typical park visitor spends at least 90 minutes in the park during summer months. A sample of 18 visitors during the summer months of 2011 revealed the mean time in the park was 96 minutes with a standard deviation of 12 minutes. At the 0.01 significance level, is it reasonable to conclude that the mean time in the park is greater than 90 minutes? What is alpha?

Stepfall Ltd had the following ratios at 31 December 2017 and 31 December 2016: 2017 2016 Gross profit margin 27% 31% Return on capital employed 15% 22% Current ratio 1.1:1 0.7:1 Acid test ratio 0.8:1 0.6:1 Trade receivable days 33 days 48 days Inventory holding days 42 days 57 days Which ONE of the following statements is TRUE?

You are the manager of a theater. At present, the theater charges the same admission price of $8 to all customers, regardless of age. You propose a two-tier pricing scheme: $5 for children under the age of 12 and $10 for adults. You tell your supervisor that your proposal is likely to increase revenue. "What must be true about the price elasticity of demand if your proposal is to achieve its goal of raising revenue?

1) Explain the concepts of cross-price elastic of demand, using one of the examples in the table above. What does a positive or negative value indicate? When doing elasticity of demand what is the sign always for a normal good?

2)Explain the concepts of income elasticity using one of the items in the table above. What does a positive value indicate? What about a negative value indicate?

3) When the price of Bob’s Coffee House increased by 8 percent, the quantity demanded of Alex’s Coffee House increased by 10 percent. What would be the cross- price elastic of demand between Bob’s & Alex’s coffee? What is the relationship between these two goods (are they compliments?)

4) Suppose the current price of oil is $90 a barrel and the quantity supplied is 800 million barrels per day. If the price elasticity of supply for oil in the short run is estimated at 0.5, use the midpoint formula to calculate the percentage change in quantity supplied when the price of oil rises to $98 a barrel.

Tombro Industries is in the process of automating one of its plants and developing a flexible manufacturing system. The company is finding it necessary to make many changes in operating procedures. Progress has been slow, particularly in trying to develop new performance measures for the factory. In an effort to evaluate performance and determine where improvements can be made, management has gathered the following data relating to activities over the last four months: Month 1 2 3 4 Quality control measures: Number of defects 201 179 140 98 Number of warranty claims 62 55 46 43 Number of customer complaints 118 112 95 74 Material control measures: Purchase order lead time 10 days 9 days 7 days 5 days Scrap as a percent of total cost 1 % 1 % 2 % 3 % Machine performance measures: Machine downtime as a percentage of availability 5 % 6 % 6 % 10 % Use as a percentage of availability 94 % 91 % 88 % 84 % Setup time (hours) 10 12 13 14 Delivery performance measures: Throughput time ? ? ? ? Manufacturing cycle efficiency (MCE) ? ? ? ? Delivery cycle time ? ? ? ? Percentage of on-time deliveries 95 % 94 % 91 % 88 % The president has read in industry journals that throughput time, MCE, and delivery cycle time are important measures of performance, but no one is sure how they are computed. You have been asked to assist the company, and you have gathered the following data relating to these measures: Average per Month (in days) 1 2 3 4 Wait time per order before start of production 9.0 10.9 12.0 14.0 Inspection time per unit 0.9 0.8 0.8 0.8 Process time per unit 3.2 2.7 2.0 1.1 Queue time per unit 3.6 5.0 6.6 8.4 Move time per unit 0.3 0.6 0.6 0.7 Required: 1-a. Compute the throughput time for each month. 1-b. Compute the manufacturing cycle efficiency (MCE) for each month. 1-c. Compute the delivery cycle time for each month. 3-a. Refer to the inspection time, process time, and so forth, given for month 4. Assume that in month 5 the inspection time, process time, and so forth, are the same as for month 4, except that the company is able to completely eliminate the queue time during production using Lean Production. Compute the new throughput time and MCE. 3-b. Refer to the inspection time, process time, and so forth, given for month 4. Assume that in month 6 the inspection time, process time, and so forth, are the same as in month 4, except that the company is able to eliminate both the queue time during production and the inspection time using Lean Production. Compute the new throughput time and MCE.