20250519 Statistics class assignment: Example 9.3.1 two samples t-test

 

 Source:

 9.3: Independent Samples for Two Means

Kathryn Kozak

Coconino Community College

 Example 9.3.1 hypothesis test for two means

 

 Calculated by using google sheet

Cholesterol Level of Heart Attack Patients	Cholesterol Level of Healthy Individual
270	196
236	232
210	200
142	242
280	206
272	178
160	184
220	198
226	160
242	182
186	182
266	198
206	182
318	238
294	198
282	188
234	166
224	204
276	182
282	178
360	212
310	164
280	230
278	186
288	162
288	182
244	218
236	170
	200
	176
Mean, x1-bar	Mean, x2-bar
253.9285714	193.1333333
s1: sample SD	s2: sample SD
47.71049156	22.30004381
n1	n2
28	30

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 Using an online application: 

 

Mann Whitney U test calculator (Wilcoxon rank-sum)

 

 

 

1. H₀ hypothesis
Since p-value < α, H₀ is rejected.
The randomly selected value of Group1's population is considered to be not equal to the randomly selected value of Group2's population.
In other words, the difference between the randomly selected value of Group1 and the Group2 populations is big enough to be statistically significant.

2. P-value
The p-value equals 0.000001057, ( p(x≤Z) = 1 ). It means that the chance of type I error (rejecting a correct H₀) is small: 0.000001057 (0.00011%).
The smaller the p-value the more it supports H₁.

3. The statistics
The test statistic Z equals 4.8808, which is not in the 99% region of acceptance: [-2.5758 : 2.5758].
U=734, is not in the 99% region of acceptance: [254.5507 : 585.4493].

4. Effect size
The observed standardized effect size, Z/√(n₁+n₂), is large (0.64). That indicates that the magnitude of the difference between the value from Group1 and the value from Group2 is large.
The observed common language effect size, U₁/(n₁n₂), is 0.87, this is the probability that a random value from Group1 is greater than a random value from Group2.
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The same source

Example 9.3.3 hypothesis test for two means

 

Sodium in Beef Hotdogs	Sodium in Poultry Hotdogs
495	430
477	375
425	396
322	383
482	387
587	542
370	359
322	357
479	528
375	513
330	426
300	513
386	358
401	581
645	588
440	522
317	545
319	430
298	375
253	396

 

This time, we use 

 https://www.graphpad.com/quickcalcs/ttest2/

 To run unpaired t-test

 

 

P value and statistical significance:

The two-tailed P value equals 0.1015
By conventional criteria, this difference is considered to be not statistically significant.

Confidence interval:

The mean of Group One minus Group Two equals -49.05
95% confidence interval of this difference: From -108.21 to 10.11

Intermediate values used in calculations:

t = 1.6783
df = 38
standard error of difference = 29.226

Review your data:

Group

Mean
SD
SEM
N

Group One

401.15
102.43
22.91
20    

Group Two

450.20
81.18
18.15
20     

 

 -----------conclusion

 p-value > alpha   (fail to reject Ho)

In other words, there is no evidence to show that the sodium in beef hotdogs is less than poultry hotdogs