T- T EST Prof. Dr. Ramez Bedwany

C OMPARISON OF TWO INDEPENDENT SAMPLES T - T EST = 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

E XAMPLE (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

A NSWER n1=25 X1=125 S1=10 n2=17 X2=132 S2=12 df= n1+n2-2 = =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 %

E XERCISE 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 difference n = sample size Critical t from table at df = n-1

E XAMPLE (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

ANSWER

= =

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

A SSIGNMENT محمد احمد فتوح احمد محمد صالح السيد محمد عادل خضر محمد علي رمضن Measures of Dispersion

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