Answered: You wish to test the following claim…

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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Question

You wish to test the following claim (HaHa) at a significance level of α=0.01. For the context of this problem, μd=μ2−μ1 where the first data set represents a pre-test and the second data set represents a post-test.

Ho:μd=0
Ha:μd≠0

You believe the population of difference scores is normally distributed, but you do not know the standard deviation. You obtain the following sample of data:

pre-test	post-test
62	54.8
43.7	37.7
67.2	46
59.9	33.2
37.5	44.9
30.6	24
49	41.2

What is the critical value for this test? (Report answer accurate to three decimal places.)
critical value = ±

What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic =

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Expert Solution

Step 1

Step-by-step procedure to obtain the test statistic and critical-value using Excel:

In Excel sheet, enter Pre-test in one column and enter Post-test in one column.
In Data, select Data Analysis and choose t-test; Paired Two samples for means.
In Input Variable 1 Range, select Post-test.
In Input Variable 2 Range, select Pre-test.
In Hypothesized Mean Difference, enter 0.
Enter 01 under Alpha and click Labels.
Click Ok.

Step 2

Output obtained using Excel is given below:

t-Test: Paired Two Sample for Means
post-test
pre-test
Mean
40.25714 49.98571429
Variance
97.92619 185. 1914286
Observations
7
7
Pearson Correlation
0.589042
Hypothesized Mean Difference
0
df
6
t Stat
-2.30711
P(T<=t) one-tail
0.030254
t Critical one-tail
3.142668
P(T<=t) two-tail
0.060508
t Critical two-tail
3.707428

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