Answer:
Let x = number of units produced per hour before the line was modified , y = number of units produced per hour after the line was modified.
The null and alternative hypotheses are :
H0: μbefore = μafter
H1: μbefore ≠ μafter
Step 1: . Calculate the difference (D = y − x) between the two observations on each pair.
See attachment for (D=y-x)
step 2: Calculate ∑D and ∑D2
From table we get ∑D = -10 & ∑D2 = 72
Step 3: Put all the value in test statistic "t"
t = D/√nD^2-D^2/n - 1
t =-10/√6.72-(-10)^2/6-1
t= -10√66.4
= -10/8.1486
= -1.227
Step 4: Compare tcal and ttab
At α = 0.05
t0.05 for 5 d.f. = 3.1634 (two tail test)
Hence | tcal | < t0.05
So, we accept the hypothesis.
So we conclude that the modified (after) layout has not increased worker productivity at 5% level of significance.
The slope of the line passes through (-6, 3) and (1, 5) is 
<u>Solution:</u>
Given, two points are (- 6, 3) and (1, 5)
We have to find the slope of a line that passes through the above given two points
Slope of a line that pass through 
is given as:
Hence, the slope the line that passes through the given points is
The measurement of angle a plus 120 must equal to 180 ( as angles on a straight line must equal to 180)
So measurement of angle a is 60 degrees
Measurement of angle b plus 60 plus 60 must equal to 180
So measurement of angle b is 60
A graph is a way to represent a lot of data in a visual format. thus the number of games in the category 51-57 are 3.
<h3>What is a graph?</h3>
A graph is a way to represent a lot of data in such a visual format that it is easy for the user to understand the complete information in one go. the line of the graph is a function that follows the graph.
The categories and the data points can be arranged as;
51 - 57 = 51, 56, 55
58 - 64 = 63, 59, 60, 64
65 – 71 = 70, 67
72 or more = 75
Therefore, the number of games in the category 51-57 are 3.
Learn more about Graph:
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