1.The number of cars passing eastbound through the intersection of Mill and University Avenues has been tabulated by a group of civil engineering students. They have obtained the data in the adjacent table.
Vehicles
per Minute
Observed
Frequency
Vehicles
per Minute
Observed
Frequency
40
14
53
102
41
24
54
96
42
57
55
90
43
111
56
81
44
194
57
73
45
256
58
64
46
296
59
61
47
378
60
59
48
250
61
50
49
185
62
42
50
171
63
29
51
150
64
18
52
110
65
15
In this problem, you’ll be testing whether the above data reflects a Poisson distribution.
a.Derive the maximum likelihood estimator for a Poisson Distribution with parameter l.
b.Using your answer from part 1, if we assume the data does reflect a Poisson Distribution, find the estimator for l.
c.Create an appropriate histogram of the data. Use as many buckets as you think is appropriate.
d.Using the results from parts (2) and (3), and the provided data, run an appropriate test to determine whether the data comes from a Poisson Distribution.
2.Consider the data below.
Hours Studied
1
0
3
1.5
2.75
1
0.5
2
3
1.75
Test Score
76
66
96
84
100
81
85
79
100
81
a.Using Least-Squares regression, find the line of best fit that uses Hours Studied to predict a Test Score.
b.Create a scatterplot of the data and draw your line from part (a).
c.Find SSE, SSR, and SST.
d.Find the Coefficient of Determination, and give a brief interpretation of the answer.
e.Test whether both the intercept and slope parameters are 0. Use α = 0.05
f.We define regression correlation as, where XY is the covariance between Y and X.
It can be determined that, and a correlation is considered Strong if |is above .5. In other words, the sample correlation coefficient is the square root of R2. Find the sample correlation.
g. Run an appropriate test to determine whether this correlation is 0. The test statistic, , has degrees of freedom n-2.
- Two different analytical tests can be used to determine the impurity level in steel alloys. Eight specimens are tested using both procedures, and the results are shown in the following tabulation. Is there sufficient evidence to conclude that both tests give the same mean impurity level, using α = 0.01? Round numeric answer to 2 decimal places.
Specimen
Test 1
Test 2
1
1.4
1.6
2
1.5
1.9
3
1.7
1.7
4
1.4
1.3
5
1.9
2.2
6
2
2.3
7
1.6
1.9
8
1.5
1.8
4.Consider the data from problem (3). If we could not assume the data came from a paired test, would you reach the same conclusion? Run an appropriate Hypothesis test with α = 0.01.
Sample Solution
