Data of variable-A is collected as shown to the right.Is the mean of Variable-A less than 80? State null hypothesis and choose level of significance, a = 0.05. (Use Excel ttest function, provide clear logic and reasoning.)Variable-AVariable-B78.881.976.978.067.869.768.974.770.570.080.068.263.088.778.786.785.469.587.075.182.471.878.258.176.974.860.293.282.684.667.266.571.777.268.974.069.377.789.178.676.368.374.089.069.482.176.378.066.280.373.982.479.183.180.466.466.267.680.975.3

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Description: Data of variable-A is collected as shown to the right.Is the mean of Variable-A less than 80? State null hypothesis and choose level of significance, a = 0.05. (Use Excel ttest function, provide clear logic and reasoning.)Variable-AVariable-B78.881.9

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Data of variable-A is collected as shown to the right.

Is the mean of Variable-A less than 80? State null hypothesis and choose level of significance, a = 0.05. (Use Excel ttest function, provide clear logic and reasoning.)

Variable-A	Variable-B
78.8	81.9
76.9	78.0
67.8	69.7
68.9	74.7
70.5	70.0
80.0	68.2
63.0	88.7
78.7	86.7
85.4	69.5
87.0	75.1
82.4	71.8
78.2	58.1
76.9	74.8
60.2	93.2
82.6	84.6
67.2	66.5
71.7	77.2
68.9	74.0
69.3	77.7
89.1	78.6
76.3	68.3
74.0	89.0
69.4	82.1
76.3	78.0
66.2	80.3
73.9	82.4
79.1	83.1
80.4	66.4
66.2	67.6
80.9	75.3

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

Expert Solution

Step 1

Data of variable-A is entered in a spreadsheet.

Therefore,

sample mean = $x$ = 74.87

This is calculated using the '=AVERAGE(cell range)' function.

sample standard deviation = s = 7.24

This is calculated using the '=STDEV.S(cell range)' function.

Let the population mean be $μ$

The data size (n) is given to be 30.

The null hypothesis to be tested for this problem is -

$H_{0} : μ = 80$

while the alternative hypothesis is-

$H_{1} : μ < 80$

level of significance a is given to be 0.05.

From the alternative hypothesis it can be said that the test being performed is the left-tailed test.

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