A test is conducted on 25 lemon trees of the same species to compare two fertilizers, A and B. A sample of 13 lemon trees randomly selected from the group are given fertilizer A and the remaining trees are given fertilizer B. From observations made over a three-week period, the average fruits produced by each lemon tree is recorded below:

Lemon Fruit Yield (for each tree)
fertilizer A (x1) 44 44 56 46 47 38 58 53 49 35 46 30 41
fertilizer B (x2) 35 47 55 29 40 39 32 41 42 57 51 39

Assume these two samples come from independent normally distributed populations.

6) Find the mean number of lemons for fertilizer A rounded to the tenths place.

7) Find the mean number of lemons for fertilizer A rounded to the tenths place.

Now perform the two-sample t-test to investigate the evidence of a difference in true mean lemon yields for the two fertilizers.

8) Using a pooled variance, find the p-value.

9) Which of the following hypotheses are most appropriate in determining whether there is a difference in the true mean lemon yields for the two fertilizers? (Choose 2)

• Ho: μ1 = μ2

• Ho: μ1 ≠ μ2

• Ha: μ1 = μ2

• Ha: μ1 ≠ μ2

• Ho: μ1 > μ2

• Ho: μ1< μ2

• Ha: μ1 > μ2

• Ha: μ1 < μ2

1. Justine runs a business selling hockey sticks in Canada and generally expects to sell about $15,000 worth of sticks per month (Canadians play roller hockey in the summer).  In June, she runs a radio advertising campaign which costs $1500.  As part of her advertising campaign she offers a $5 discount on any hockey stick (the sticks retail for $50 normally with a margin of 35%).  In June she records sales of $22,005.
   

1. What is the lift % from the advertising campaign in both dollars and units?
2. What is the cost to Justine per incremental sales dollar she saw if you ignore the discount?
3. What is the Return on Marketing Investment if you factor in the discount?
4. If she could get the manufacturer to drop the price she pays for hockey sticks by $1.50, what would be the pass through percentage of her discount?

A company wants to determine whether its consumer product ratings

​(0minus−​10)

have changed from last year to this year. The table below shows the​ company's product ratings from eight consumers for last year and this year. At

alphaαequals=​0.05,

is there enough evidence to conclude that the ratings have​ changed? Assume the samples are random and​ dependent, and the population is normally distributed. Complete parts​ (a) through​ (f).

Q1. Compressors powered by natural gas engines are increasing in popularity. Several major manufacturing facilities have already replaced the electric motors that drive their compressors with gas-driven engines in order to reduce their energy bills since the cost of natural gas is much lower than the cost of electricity. Consider a facility that has a 130-kW compressor that runs 4400 h/yr at an average load factor of 0.6. Making reasonable assumptions and using unit costs for natural gas and electricity at your location, determine the potential cost savings per year by switching to gas-driven engines. (TOTAL 25 MARKS)

Is HDTV ownership related to quantity of purchases of other electronics? A Best Buy retail outlet collected the following data for a random sample of its recent customers. At α = 0.10, is the frequency of in-store purchases independent of the number of large-screen HDTVs owned (defined as 50 inches or more)?

Calculate the chi-square test statistic, degrees of freedom, and the p-value.

Using Python provide the implementation of a function called "isAdjacent" that accepts a string.   The function checks if two adjacent characters in the string are the same; if they are the same, then return True otherwise return False.   The function should ignore case and check for non-empty string.  If it's an empty string, then return the message 'Empty string'.

Sample runs:

print( isAdjacent('ApPle')) # True
print( isAdjacent('Python')) # False
print( isAdjacent('')) # Empty string

Jim is a transportation engineer and is interested in whether roadways that score high in one traffic engineering aspect also tend to score high in other aspects. To address this question, he completed a survey of 80 roadways that contain five measures of effectiveness with ratings for safety, capacity, speed, alignment, and flow.

a) Conduct a correlational analysis to investigate these relationships. What are your conclusions?

b) Jim determines that the speed of a facility affect/s the other roadway scores. Reevaluate Jim's hypothesis by controlling for speed. What effect does partialling out the effects of speed have on the relationships?

safety capacity speed alignment flow

48   56   48   35   47
44   50   47   41   51
38   41   49   59   46
48   59   59   49   52
44   44   52   37   47
43   57   42   52   54
49   53   56   32   49
52   65   57   54   54
55   63   56   58   53
50   60   49   52   54
45   47   44   51   49
61   56   57   63   50
49   57   50   51   50
44   45   46   31   47
39   50   51   28   52
50   51   51   43   54
49   51   50   50   49
37   52   44   45   53
49   55   51   47   53
47   48   46   44   54
55   56   55   42   54
49   60   62   58   53
45   58   65   59   54
39   40   36   44   46
54   56   51   55   52
58   58   51   44   53
52   52   62   47   53
50   56   38   47   51
62   57   52   25   53
55   55   59   57   49
50   52   52   47   53
44   35   44   46   45
55   55   39   24   48
46   45   44   54   47
48   51   47   50   50
52   52   38   53   47
52   49   50   59   49
50   49   39   40   48
48   50   52   52   43
50   45   46   36   47
50   46   44   44   52
43   40   43   27   45
40   44   54   50   47
57   67   53   41   58
57   52   56   67   58
61   62   51   60   56
46   52   52   60   56
42   44   48   41   56
60   58   66   50   57
47   47   58   51   56
50   59   51   43   57
63   65   56   63   62
59   52   42   42   56
50   52   59   57   56
49   59   62   51   61
51   52   56   44   58
47   62   67   54   66
52   62   58   47   62
60   48   55   45   63
45   45   59   47   60
59   53   51   39   57
57   51   68   59   59
46   60   64   54   57
51   61   46   44   59
47   53   49   41   55
50   63   52   48   64
57   69   70   51   57
50   57   51   37   56
65   69   62   60   55
50   58   54   49   56
56   63   54   49   58
54   65   57   38   56
42   53   47   45   56
53   53   62   49   59
61   54   57   63   61
47   56   50   58   55
46   55   48   55   57
57   54   58   58   57
56   60   51   47   58
50   52   50   46   56

1. The Pratt Corporation manufactures computer terminals. The following data give the number of computer terminals produced at the company for a sample of 30 days. 24 32 27 23 33 33 29 23 28 25 21 26 31 22 27 33 27 28 29 23 31 35 34 22 26 28 23 31 27 35 Make a frequency table showing class boundaries, class midpoints, frequencies, relative frequencies, and cumulative frequencies. What is the modal class?

2. The following date give the weight (in pounds) lost by 16 new members of a health club at the end of their first two months of membership. 5 10 8 7 25 12 6 14 11 10 21 9 8 11 18 11 Find a. Mean b. Median c. Mode

3. The following data give the weekly dinner expenditures for a sample of five students. $62 96 45 55 72 a. Find the range b. Find the sample mean. c. Find the sample variance d. Find the sample standard deviation. e. Find the CV

4. The following data give the hours worked last week by 30 employees of a company. 42 45 40 38 35 47 40 27 39 43 40 53 23 51 42 48 40 36 51 40 48 34 21 40 31 34 16 39 41 36 Give the five-number summary including the low value, Q , Median, Q and high value. Find the interquartile range and check for outliers.

5. The following are the scores of 30 college students on a statistics test. 75 52 80 96 65 79 71 87 93 95 69 72 81 61 76 86 79 68 50 92 83 84 77 64 71 87 72 92 57 98 Make a stem-and-leaf display of the data.

Company X produces an end product Afor the market. One unit of Ais made by assembling 1 unit of K, 2 units of L, and 1 unit of M. One unit of K is made of 2 units of G and 3 units of H; one unit of L is assembled using 1 unit of M and 2 units of N. Current on-hand inventories for L and M are 130 and 60, respectively. Scheduled receipts are 300 for L at the beginning of week 1 and 150 for M at the beginning of week 2.
Lead times for K and L are one week, and lead times for other components are two weeks. The final assembly time for A is one week.
1. Fill in Table 1 to prepare a master production schedule for end product Ausing a fixed lot size of 200. The beginning inventory for A is 180; the forecast and committed customer orders
for A are provided in this table.

Table 1: MPS table for end product A in Question 1

b. Construct the product structure tree (i.e., the BOM chart) for A.

c. Use your master production schedule in Table 1 to develop a material requirement plan (MRP) for the subassembly L using the lot-for-lot policy.

Thanks very much

16. A 1.8-kg projectile is fired from level ground. The vertical component of the initial velocity is 80 m/s and the horizontal component is 16 m/s. Ignore air resistance and the curvature of the earth in this problem. How far in meters does the projectile travel horizontally?

19. If one platter of lasagna uses 1.5 cups of tomato sauce, how many cups of tomato sauce will 4 platters of lasagna require?

20. A sprinter runs 53 meters in 7 seconds. What is his average speed?