Answered: For the following set of data from two…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.5: Comparing Sets Of Data

Problem 14PPS

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Question

For the following set of data from two independent samples, conduct an independent samples t test (by hand or using SPSS) to determine if the mean scores for each sample are significantly different.

Sample 1: 5, 7, 4, 7, 2, 6, 7, 3, 4, 5

Sample 2: 3, 4, 3, 4, 3, 3, 3, 4, 5, 4, 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

The hypotheses are given below:

Null hypothesis: H =2
Alternative hypothesis: H

Step 2

Step-by-step procedure to obtain the mean and standard deviation using MINITAB software:

Choose Stat > Basic Statistics > Display Descriptive Statistics.
In Variables enter the columns 8-10 year, 11 and 14 year.
Choose option statistics, and select Mean and standard deviation.
Click OK.

Output obtained using MINITAB software is given below:

Descriptive Statistics: Sample 1, Sample 2
Statistics
Variable
Sample 1 10 0 5.000
Sample 2 11
N N Mean SE Mean StDev Variance Minimum Maximum
0.558
1.764
3.111
2.000
7.000
0.688
0.473
3.545
0.207
3.000
5.000

Step 3

The degrees of freedom is,

Step 4

Step-by-step procedure to obtain the critical value using MINITAB software:

Choose Graph > Probability Distribution Plot choose View Probability > OK.
From Distribution, choose ‘t’ distribution.
In Degrees of freedom, enter 19.
Click the Shaded Area
Choose Probability and both Tail for the region of the curve to shade.
Enter the Probability as 0.05.
Click OK.

Output obtained using MINITAB software is given below:

Distribution Plot
T, df 19
0.4
0.3
0.2
0.1
0.025
0.025
0.0
-2.093
0
2.093
х
Density

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