Fuming because you are stuck in traffic? Roadway congestion is a costly item, both in time wasted and fuel wasted. Let x represent the average annual hours per person spent in traffic delays and let y represent the average annual gallons of fuel wasted per person in traffic delays. A random sample of eight cities showed the following data. x (hr) 26 5 21 37 21 20 16 5 y (gal) 45 3 34 56 31 35 28 9 (a) Draw a scatter diagram for the data Verify that Σx = 151, Σx2 = 3633, Σy = 241, Σy2 = 9377, and Σxy = 5815. Compute r. The data in part (a) represent average annual hours lost per person and average annual gallons of fuel wasted per person in traffic delays. Suppose that instead of using average data for different cities, you selected one person at random from each city and measured the annual number of hours lost x for that person and the annual gallons of fuel wasted y for the same person. x (hr) 22 4 22 45 18 26 2 36 y (gal) 63 8 15 51 22 32 4 71 (b) Compute x and y for both sets of data pairs and compare the averages x y Data 1 Data 2 Compute the sample standard deviations sx and sy for both sets of data pairs and compare the standard deviations. sx sy Data 1 Data 2 (c) Make a scatter diagram for the second set of data pairs. Verify that Σx = 175, Σx2 = 5309, Σy = 266, Σy2 = 13,424, and Σxy = 7835. Compute r:
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
Fuming because you are stuck in traffic? Roadway congestion is a costly item, both in time wasted and fuel wasted. Let x represent the average annual hours per person spent in traffic delays and let y represent the average annual gallons of fuel wasted per person in traffic delays. A random sample of eight cities showed the following data.
x (hr)
26
5
21
37
21
20
16
5
y (gal)
45
3
34
56
31
35
28
9
(a) Draw a
Verify that Σx = 151, Σx2 = 3633, Σy = 241, Σy2 = 9377, and Σxy = 5815.
Compute r.
The data in part (a) represent average annual hours lost per person and average annual gallons of fuel wasted per person in traffic delays. Suppose that instead of using average data for different cities, you selected one person at random from each city and measured the annual number of hours lost x for that person and the annual gallons of fuel wasted y for the same person.
x (hr)
22
4
22
45
18
26
2
36
y (gal)
63
8
15
51
22
32
4
71
(b) Compute x and y for both sets of data pairs and compare the averages
x y
Data 1
Data 2
Compute the sample standard deviations sx and sy for both sets of data pairs and compare the standard deviations.
sx sy
Data 1
Data 2
(c) Make a scatter diagram for the second set of data pairs.
Verify that Σx = 175, Σx2 = 5309, Σy = 266, Σy2 = 13,424, and Σxy = 7835.
Compute r:
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