T- Test

T- TEST

Prof. Dr. Ramez Bedwany

COMPARISON OF TWO INDEPENDENT SAMPLEST- TEST

= mean of the first simple = mean of the second sample = pooled Variance

= pooled Variance

Critical t from table at degree of freedom = n1+ n2-2

If n1+ n2 < 120 use t test

If n1+ n2 ≥120 use z test with the same formula

EXAMPLE (1)

Sample of size 25 was selected from healthy population , their mean BP 125 mm Hg with standard deviation of 10 mm Hg. another sample of size 17 was selected from population of diabetics their mean BP was l32mmHg, with standard deviation of 12 mm Hg Test whether there is significant difference in mean BP of diabetics and healthy individual at I % level of significance

ANSWER

n1=25 X1=125 S1=10 n2=17 X2=132 S2=12 df= n1+n2-2 = 25+17-2=40 Critical t at 40, 1% level of significance 2.704

Decision:

Since the computed t is smaller than critical t so there is no significant difference between mean BP of healthy and diabetic samples at 1 %

EXERCISE

Example 2 and 3

T- TEST FOR PAIRED OBSERVATION (T- DIFFERENCE)

Uses: To compare the means of two paired

samples

Example: Mean pulse rate before and after intake of

drug

di = difference (after-before)Sd = standard deviation of differencen = sample sizeCritical t from table at df = n-1

EXAMPLE (1)

The following data represents the reading of Systolic BP before and after administration of certain drug. Test whether the drug has an effect on BP at 1% level of significance

Serial number BP BP

Before after

  I 200

180 2 160

165 3 190

175 4 185

185 5 210

170 6 175

160

ANSWER

= -14.17

= 15.942

Critical t at df=6-1=5 and 1% level of significance = 4.032

Decision Since the computed t is smaller than critical t so

there is no significant difference between mean BP before and after administration of drug so the drug has no effect on BP at 1% level of significance

ASSIGNMENT

احمد فتوح احمد محمدالسيد صالح محمد

خضر عادل محمدرمضن علي محمد

Measures of Dispersion

OUTCOMES

By the end of this lecture, the student will be able to Know definition, uses and types of statistics.