Example of One-tailed One Sample Student's t Test

Biostatistics BI 45, Saint Anselm College

 

Step 1) State the biological question. Does it take longer than 45 seconds for a drug in pill form to dissolve in the gastric juices of the stomach?

 

Step 2) Translate the biological question into statistical hypotheses.

 

 

Step 3) State the alpha level: p<0.05 is considered significant

 

Step 4) State the statistical test.

Because we are working with a hypothetical population mean and a sample mean and we want to know about the direction of the difference between the means, we use the one-tailed One Sample t test.

 

Step 5) State the assumptions of the test.

The subjects in the sample must be randomly selected from a population. The sample data must come from a normally distributed population of observations for the variable under study.

 

Step 6) Calculate the observed t statistics from your data.

 

 

Time (sec)

d

d2

ss

var

sd

se

t

 

42.7

-2.5125

6.31265625

18.82875

2.68982143

1.64006751

0.57985143

0.36647319

 

43.4

-1.8125

3.28515625

 

 

 

 

 

 

44.6

-0.6125

0.37515625

 

 

 

 

 

 

45.1

-0.1125

0.01265625

 

 

 

 

 

 

45.6

0.3875

0.15015625

 

 

 

 

 

 

45.9

0.6875

0.47265625

 

 

 

 

 

 

46.8

1.5875

2.52015625

 

 

 

 

 

 

47.6

2.3875

5.70015625

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Sum

361.7

 

 

 

 

 

 

 

Mean

45.2125

 

 

 

 

 

 

 

n

8

 

 

 

 

 

 

 

df

7

 

 

 

 

 

 

 

Hypoth. Mean

45

 

 

 

 

 

 

 

tobs=(Sample Mean - Hypothetical Mean)/se

tobs=(45.2125-45)/.57985143

tobs=.36647319

 

Step 7) Find the df and critical value of t from the table of critical values.

 

 

 

 

Step 8) Compare the critical and observed t values and reject or do not reject the null hypothesis.

 

 

Find the actual P value

tobs=0.36< t.25(1)7=0.711

P>0.25

 

Step 9) Interpret the results of the analysis as it relates to the biological question raised in 1). The time it took for the pill to dissolve in gastric juices was not significantly longer than 45 seconds (t=0.36, df=7, one-tailed, p>0.25).

 

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Trademark and Disclaimers

Copyright © 2001 Jay Pitocchelli. All rights reserved. The contents of this page are the intellectual property of Dr. Jay Pitocchelli for distribution to students enrolled in Biostatistics BI 45 at Saint Anselm College. These pages may not be copied, photocopied, reproduced, translated, or published in any electronic or machine-readable form in whole or in part without prior written approval of Jay Pitocchelli. Students enrolled in Biostatistics BI 45 at Saint Anselm College have permission to print this material for their lecture notes. All formulae and critical values from: Zar, J. H. 1999. Biostatistical Analysis. (4th ed.). New Jersey, Prentice Hall.