4. Chapter 12: Using the attached dataset “Chapter 12 Data Set 1” to determine whether there was a change in tons of paper before vs. after a recycling program in these 25 districts. a. Is this a directional or non-directional hypothesis? b. Should you use a one-tailed or two-tailed test? c. Is a dependent samples t-test an appropriate way to analyze these data? d. Conduct the between groups t-test using Excel (either method). Use the .05 confidence level. What is your conclusion?

District   Before Recycling   After Recycling
District1   20   23
District2   6   8
District3   12   11
District4   34   35
District5   55   57
District6   43   76
District7   54   54
District8   24   26
District9   33   35
District10   21   26
District11   34   28
District12   33   31
District13   54   56
District14   23   22
District15   33   35
District16   44   41
District17   65   56
District18   43   34
District19   53   51
District20   22   21
District21   34   31
District22   32   33
District23   44   38
District24   17   15
District25   28   27

Similar to the study described on Handout 11, investigators recorded PWV, a measure of vascular stiffness, in 18 children diagnosed with progeria. The objective was to test the effectiveness of the drug lonafarnib. PWV was measured on the 18 children before taking the drug, then re-measured on the same children after receiving a daily dose of the drug for two years. Please see HW3b data, where “untreated” = before taking the drug, and “treated” = after taking the drug for two years.

a. Report the null and alternate hypotheses

b. Check assumptions of the matched pairs T-Test with a dotplot or histogram and report if it is reasonable to conduct the test

c. Run the test and report the appropriate test statistic, df, and P value

d. Based on your results from part c, do you accept or reject the null hypothesis?

e. Report the 95% CI for the mean difference between untreated and treated and interpret what this means.

A tire manufacturer warranties its tires to last at least 20 comma 000 miles or​ "you get a new set of​ tires." In its​ experience, a set of these tires last on average 28 comma 000 miles with SD 5 comma 000 miles. Assume that the wear is normally distributed. The manufacturer profits ​$200 on each set​ sold, and replacing a set costs the manufacturer ​$400. Complete parts a through c.

​(a) What is the probability that a set of tires wears out before 20 comma 000 ​miles? The probability is nothing that a set of tires wears out before 20 comma 000 miles. ​(Round to four decimal places as​ needed.)

​(b) What is the probability that the manufacturer turns a profit on selling a set to one​ customer? The probability is nothing that the manufacturer turns a profit on selling a set to one customer. ​(Round to four decimal places as​ needed.)

​(c) If the manufacturer sells 500 sets of​ tires, what is the probability that it earns a profit after paying for any​ replacements? Assume that the purchases are made around the country and that the drivers experience independent amounts of wear. The probability is nothing that the manufacturer earns a profit after paying for any replacements on 500 sets of tires. ​(Round to four decimal places as​ needed.)

Phoebe and Parker are equal members in Phoenix Investors, LLC. They are real estate investors who formed the LLC several years ago with equal cash contributions. Phoenix then purchased a parcel of land.

On January 1 of the current year, to acquire a one-third interest in the entity, Reece contributed to the LLC some land she had held for investment. Reece purchased the land five years ago for $120,000; its fair market value at the contribution date was $90,000. No special allocation agreements were in effect before or after Reece was admitted to the LLC. Phoenix holds all land for investment.

Immediately before Reece’s property contribution, the balance sheet of Phoenix Investors LLC was as follows:

        Basis FMV

Land $30,000 $180,000

Phoebe, capital 15,000    90,000

Parker, capital 15,000    90,000

A few years later, Pheonix sold the land contributed by Reece for 84,000

A. How much is the recognized gain or loss? how is it allocated among the LLC members

B. Prepare a balance sheet reflecting basis and fair market value for the LLC immediately after the land sale. Also prepare schedules that support the basis and fair market value of each LLC members capital account.

ch15.2

The accompanying data show spot speeds collected at a section of highway located in a residential area. (i) Using the student’s t test, determine whether there was a statistically significant difference in the average speeds at the 95% confidence level. (ii) Also report for before and after the following: mean speed, standard deviation, 85^th percentile speed and percentage of traffic exceeding the posted speed limit of 30 MPH. (iii) using the data, draw the histogram frequency distribution, cumulative percentage distribution for each set of data and determine: (a) average speed (b) 85^th percentile speed, (c) 15^th percentile speed, (d) mode (e) median and (f) pace[the most common 10 MPH range].

A stationary bicycle wheel of radius 0.7 m is mounted in the vertical plane (see figure below). The axle is held up by supports that are not shown, and the wheel is free to rotate on the nearly frictionless axle. The wheel has mass 4.1 kg, all concentrated in the rim (the spokes have negligible mass). A lump of clay with mass 0.5 kg falls and sticks to the outer edge of the wheel at the location shown. Just before the impact the clay has speed 6 m/s, and the wheel is rotating clockwise with angular speed 0.29 rad/s. (Assume +x is to the right, +y is upward, and +z is out of the page. Assume the line connecting the center to the point of impact is at an angle of 45° from the horizontal.)

(a) Just before the impact, what is the angular momentum (magnitude and direction) of the combined system of wheel plus clay about the center C?

(b) Just after the impact, what is the angular momentum (magnitude and direction) of the combined system of wheel plus clay about the center C?

(c) Just after the impact, what is the angular velocity (magnitude and direction) of the wheel?