Using a graphing calculator or computer software package, estimate and verify the mathematical solutions for one of the following problems:

1. The following data show the commuting distances and commuting times of six college students to their college campus.

1. Determine the correlation coefficient between the commuting distance and the commuting time.

2. Determine whether a correlation exists at a = 0.05.

3. Determine the equation of line of best fit for the commuting distance and the commuting time.

Take a picture of your graphing calculator or a screen shot of an online calculator/software package and attach to the assignment. Please cite any extra sources, including which software you are using (graphing calculator, Excel, Desmos, etc.) Be sure to include your name on your project. Please cite all resources.

A manufacture in Ontario has been fined because it has been releasing 5 L/s effluent having
zinc concentration of 0.1 mg/L into a river. Upstream of the factory, the stream water rate is
100 L/s with zinc concentration of approximately zero. The factory has been forced to
reduce the zinc concentration of the effluent to below 20 μg/L. The engineer that is an
employee of the factory recommends that they divert parts of the stream into the site and
dilute the effluent to bring its zinc concentration to the required level.

a) Calculate the present concentration of zinc several miles downstream of the plant
where the zinc is diluted in stream completely.

b) Compute the amount of water needed to be diverted to the site to achieve the required
zinc concentration of effluent.

c) Determine the concentration of zinc downstream of the plant where the zinc is diluted
in stream completely if the engineer’s plan is put into operation.

For the mtcars dataset (in R), comment on how Rear axle ratio is associated with Displacement (cu.in.) and Miles/(US) gallon using the following steps:

1. Draw appropriate scatterplot(s) [Show your code in “R Code” section. Leave “Answer” section blank. Justify your choice of charts in a few sentences in “Comments” section. No screenshots of the charts are required.]

2. Determine correlation coefficient(s) [Show your code in “R Code” section. Show the answer in “Answer” section. Leave “Comments” section blank.]

3. Calculate and plot appropriate regression lines [Show your code in “R Code” section. Leave “R Code” and “Comments” section blank.]

4. Comment on how the variables are associated with each other [Leave “R Code” and “Answer” section blank. Include the phrase “associated” or “not associated” along with a justification in a few sentences in “Comments” section.]

The accompanying table shows a portion of a data set that refers to the property taxes owed by a homeowner (in $) and the size of the home (in square feet) in an affluent suburb 30 miles outside New York City.

a. Estimate the sample regression equation that enables us to predict property taxes on the basis of the size of the home.

TaxesˆTaxes^ = ____ + _____ Size.

c. Predict the property taxes for a 1,500-square-foot home. (Round coefficient estimates to at least 4 decimal places and final answer to 2 decimal places.)

  Taxesˆ_______

A new model compact car is being tested for gasoline consumption. A random sample of 40 such cars were tested at the sea level and found to get an average of 36.2 m/g (miles
per gallon) with a sample standard deviation of 4.8 m/g. Another random sample of 35 such cars were tested one mile above the sea level in Denver, CO., and found to get an average of 31.5 m/g with a sample standard deviation of 5.5 m/g. At the 0.01 level of significance, test the claim that the new model compact cars burn more gas (get less m/g on average) at one mile above sea level.

Sample 1 Sample 2
Claim:
1- H0:
H1:
2- Test Statistic:

3- Critical Region/Critical Value:

4- Decision about H0

1 (20 pts) You are working for NASA/JPL on the Juno mission. Juno is a large spacecraft orbiting Jupiter.
It's current distance from Earth is 536 million miles. Assume the speed of light is c = 2:0 108 m/s. The
transfer rate from Juno to Earth is 50 Mbps. The frame is made up of a 24 byte header plus a variable size
payload of 1 - 1000 bytes. Answer the following:

(a) The total transmission time to send 128 GB of pictures to Earth. Assume only transmission time and
propagation delay.
(b) The amount of time required to transfer the pictures taking in to account propagation delay, transmis-
sion delay, queuing delay, and processing delay. Queuing delay is 1 ms per frame and processing delay
is 0.5 ms per frame

Can a low barometer reading be used to predict maximum wind speed of an approaching cyclone? Data for this problem are based on information taken from Weatherwise, a publication of the American Meteorological Society. For a random sample of tropical cyclones, let x be the lowest pressure (in millibars) as a cyclone approaches, and let y be the maximum wind speed ( in miles per hour) of the cyclone x 1004 975 992 935 985 932 Y 40 100 65 145 80 150
a. (2 pts.) Make a scatter diagram and draw a line you think best fits the data.
b. (3 pts.) Find the sample correlation coefficient r.
c. (3 pts.) Find the equation for the least squares regression line
d. (2 pts.) Find the maximum wind speed when the barometric pressure is 950.

As part of an evaluation program, a sporting goods retailer wanted to compare the downhill coasting speeds of 4 brands of bicycles. She took 3 of each brand and determined their maximum downhill speeds. The results are presented in miles per hour in the table below.

Trial Barth Tornado Reiser Shaw

1 43 37 41 43
2 46 38 45 45
3 43 39 42 46

Data are analyzed by One-Way Anova. The conclusion is:

a) at the 0.01 level of significance, the mean speeds for the 4 brands are all the same.
b) at the 0.05 level of significance, there is no difference between mean speeds for the 4 brands.
c) at the 0.05 level of significance, the mean speeds for the 4 brands are not significantly different from 0.
d) at the 0.01 level of significance, the mean speeds for the 4 brands are not all the same.

Actions for Discussion Activity #5 Assume the following planned changes in (market) prices: (i).A State (Public) University you are currently attending has decided to raise tuition by 10% next semester. (ii). The Parking department at the university will increase the parking fee for the guaranteed but limited parking space on campus by 20% next academic year. Your home town (where you commute from) is 25 miles away from campus. (iii). The Campus bookstore will increase the prices of new textbooks, which you are required to buy, by 25%, next semester. (iv) . Your favorite restaurants down town will raise their menu prices by 10%, next month. Assuming that you have a limited (fixed) amount of income, Indicate how you are likely to respond to the above price changes? Briefly explain whether (your) demand is “elastic” or "inelastic” ,in each of the above cases?