Find the mean ( average):
105 + 104 + 110 + 112 + 114 + 106 + 108 +109 = 868
Mean = 868 / 8 = 108.5
Standard deviation:
108.5 - 105 = 3.5, 3.5^2 = 12.25
108.5 - 104 = 4, 4^2 = 16
110 - 108.5 = 1.5, 1.5^2 = 2.25
112 - 108.5 = 3.5, 3.5^2 = 12.25
114 - 108.5 = 5.5, 5.5^2 = 30.25
108.5 - 106 = 2.5, 2.5^2 = 6.25
108.5 - 108 = 0.5, 0.5^2 = 0.25
109 - 108.5 = 0.5, 0.5^2 = 0.25
12.25 + 16 +2.25 + 12.25 + 30.25 +6.25+0.25+0.25 = 79.75
79.75/8 = 9.96875, SQRT(9.96875) = 3.1573
Standard Deviation = 3.1573
108.8 +/- 1.96 *(3.1573/sqrt(8) = 110.687 and 106.312
110.687 - 108.5 = 2.19
108.5 - 106.312 = 2.19
Margin of error = +/- 2.19
Answer:
108.50 divided by 14= 7.75
Step-by-step explanation:
Answer:
The decision rule is
Fail to reject the null hypothesis
The conclusion is
There is no sufficient evidence to show that the designer's claim of a better shoe is supported by the trial results.
Step-by-step explanation:
From the question we are told that
The population mean is 
The sample size is n = 25
The sample mean is 
The standard deviation is 
Let assume the level of significance of this test is 
The null hypothesis is 
The alternative hypothesis is 
Generally the degree of freedom is mathematically represented as

=> 
=> 
Generally the test statistics is mathematically represented as

=> 
=> 
Generally from the student t distribution table the probability of obtaining
to the right of the curve at a degree of freedom of
is

From the value obtained we see that
hence
The decision rule is
Fail to reject the null hypothesis
The conclusion is
There is no sufficient evidence to show that the designer's claim of a better shoe is supported by the trial results.
The base length of the triangle is 10 ft. and the height of the triangle is 20ft.
Step-by-step explanation:
Height = base + 10
Area = 100 square ft
Area of a triangle= (1/2) (b) (h)
100 = (1/2) (b) (b + 10)
200 = b(b) + 10b
b(b) + 10b - 200 = 0
b(b) + 20b - 10b - 200 = 0
b ( b + 20) -10(b + 20) = 0
(b-10) (b+20) =0
b = 10 (or) b = -20
Here b is the length and cannot be negative.
So, b = 10ft
h = b + 10
h = 10 + 10
h = 20 ft.
The base length of the triangle is 10 ft. and the height of the triangle is 20ft.
Answer:n=-t+m
Step-by-step explanation: