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Identify a research problem different from the previous research problems that uses two different sets of the same type of data
I4 (Week 4) Individual Assignment: t-test I4: Identify a research problem different from the previous research problems that uses two different sets of the same type
of data. Any subject may be chosen. Some examples: Sales from two different months or years. GPA’s of men and women. Number of two different shelf items sold (Coke &
Pepsi) by month over a year. Home sales prices in different suburbs, cities, counties or states. You wish to determine if there is a significant difference between the
means of the data sets. Select data that have absolute zero measurements (Ratio data). You may use recorded data or made up data. The n sample size should be at least
10 in each set, but not more than 29. Prepare a paper with a table of contents. Describe the research problem, research purpose and one research question. Include a
definition of the variables you are measuring. List the data. List alpha, the null and alternative hypothesis, and give a brief back ground. Do MegaStat descriptive
statistics on the data and do data analysis describing the data. Do runs plot graphs. Interpret the Goodness of Fit (GOF) p-value to decide if the data is parametric
(normal) or nonparametric.
t-test: Open Excel, log in both data sets. Go to Add Ins, Megastat, Hypothesis Tests, Compare Two Independent Groups, left mouse click highlight Group 1 then Group 2,
OK. Conclude. Use the I4 sample as a guide. This paper should be between 900-1200 words. Post as an Individual assignment. Title the document file “t-test I4”.
Attachments:

How to do a t-test with Megastat
t-tests were developed by William Gossett to discover if there is a significant difference in the means of data. Although there are many types of t-tests you will
compare two independent groups. The data samples must be under 30. No not have zero’s or words (nominal data, women, men, etc.) in your data sets.
See slides 102-107 in Power Point Presentation in the Instructor Announcements under Yellow Brick Road.
See the t-test sample paper and Megastatsin the Student Materials.
First understand that you must have two different sets of the same type of data. You can compare apples and oranges as long as you measure their weight or total sales
but you cannot compare weight and sales. They will certainly be different. Example below: Electric and gas monthly heating costs measuring U.S. dollars.
Electric Gas
265 260
271 270
260 250
250 255
248 250
280 275
257 260
262 260

Open Excel, log in both data sets. Go to Add Ins, Megastat, Hypothesis Tests, Compare Two Independent Groups, left mouse click highlight Group 1 then Group 2, OK.
This will appear in the output tab at the bottom of the spreadsheet:
Hypothesis Test: Independent Groups (t-test, pooled variance)

Electric Gas
261.57 260.00 mean
11.41 8.86 std. dev.
7 8 n

13 df
1.571 difference (Electric – Gas)
102.440 pooled variance
10.121 pooled std. dev.
5.238 standard error of difference
0 hypothesized difference

0.300 t
.7689 p-value (two-tailed)

Retain the null hypothesis, the p-value of p=.76 is larger than the alpha level of significance of .05. There is no significant difference between electric and gas as
measured by monthly heating costs.

Copy and paste to your paper.
Use p-value in the Student Materials and slides 66-69 in Power Point Presentation in the Instructor Announcements under Yellow Brick Road to help you reject or retain
the null hypothesis to determine if the data sets are significantly different or the same.
I hope this helps,

Dr. Loro

FIELD # 1 FIELD # 2 Descriptive statistics
24.00 22.00
25.00 23.00 FIELD # 1 FIELD # 2
22.00 20.00 count 10 10
25.00 19.00 mean 24.0000 21.8000
24.00 21.00 sample standard deviation 1.0541 1.9322
25.00 24.00 sample variance 1.1111 3.7333
23.00 23.00 minimum 22 19
24.00 24.00 maximum 25 24
25.00 19.00 range 3 5
23.00 23.00
standard error of the mean 0.3333 0.6110

confidence interval 95.% lower 23.3467 20.6024
confidence interval 95.% upper 24.6533 22.9976
margin of error 0.6533 1.1976
z 1.96 1.96

skewness -0.7115 -0.4575
kurtosis -0.4500 -1.4124
coefficient of variation (CV) 4.39% 8.86%

normal curve GOF
p-value .0578 .1573
chi-square(df=1) 3.600 2.000
E 2.500 2.500
O(-0.67) 3 3
O(+0.00) 3 1
O(+0.67) 0 4
O(inf.) 4 2

Hypothesis Test: Independent Groups (t-test, pooled variance)

FIELD # 1 FIELD # 2
24.0000 21.8000 mean
1.0541 1.9322 std. dev.
10 10 n

18 df
2.20000 difference (FIELD # 1 – FIELD # 2)
2.42222 pooled variance
1.55635 pooled std. dev.
0.69602 standard error of difference
0 hypothesized difference

3.161 t
.0054 p-value (two-tailed)

14 df
1.625 difference (Electric – Gas)
95.134 pooled variance
9.754 pooled std. dev.
4.877 standard error of difference
0 hypothesized difference

p-VALUES &ALPHA
P-values are at first difficult to understand. They are the answer to your research question and hypothesis. See attached slides 66-69 in the power point presentation
in Instructor Announcements Yellow Brick Road.

EXCEL MEGASTAT P-VALUES RELATION TO ALPHA & THE REJECT/RETAIN DECISION
REJECT @ .01 (BRIGHT YELLOW) RETAIN @ .01 (BLACK & WHITE)
←————————————————-/—————————————————————————-→
.01
REJECT@ .05 (BRIGHT YELLOW) RETAIN @ .05 (BLACK & WHITE)
←———————————————————————————/——————————————-→
.05

←——————————————-/———————————–/———————————————→ .01
.05
(DULL YELLOW)
IF BETWEEN .011 AND .049
RETAIN @ .01 & REJECT @ .05
CAUTION – THE ALPHA LEVEL COULD FLIP THE DECISION
If the p-value is greater than Alpha: Retain the null. If the p-value is less than Alpha: Reject the null.
We reject the null hypothesis at the .05 alpha level of significance (p=.002). There is a difference between ….
We retain the null hypothesis at the .05 alpha level of significance (p=.15). There is no difference between ….
If the p-value = 1.56 E-5 that is Megastat saying the p-value is .00000156. It is 1.56 with 5 zero’s. A very small number. It is also bright yellow. Reject. There is a
significant difference.

ALPHA JUSTIFICATIONS
The nominal Alpha criterion level is set at .05 by this author as a reasonable probability for detecting a type I error.
The Alpha level of significance is set at .05 as directed by management.
The Alpha level of significance is set at .05 as indicated in previous research.
The Alpha level is set at .05 as this researcher’s conviction of the importance of this study.
The Alpha level of significance is set at .05 as used in prior research.
The Alpha level is resolved to be .01 as determined by the seriousness of this problem.
The Alpha level is .01 because injury and loss of human life is a possibility.
The Alpha level is resolved to be .01 because of the importance of this issue to the company.
The Alpha level is .01 because the loss may amount to 100 million dollars.

(The underlined words may be changed).