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T-Test. Faisal Aziz. T-Test. William S. Gosset discovered T-distribution in 1906 T-distribution is similar to normal distribution Used when sample size <30. T-Test. To compare means Numerical Data Comparing the Mean of two groups Also referred as student t-test. Degrees of Freedom.

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## T-Test

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**T-Test**Faisal Aziz**T-Test**• William S. Gosset discovered T-distribution in 1906 • T-distribution is similar to normal distribution • Used when sample size <30.**T-Test**• To compare means • Numerical Data • Comparing the Mean of two groups • Also referred as student t-test**Degrees of Freedom**Minimum number of information required to estimate the population variance One sample • n-1 Two sample • n1+n2-2**1) Determine the type of hypothesis**Right sided Steps of T-Test**Steps of T-Test**1) Determine the type of hypothesis • Left sided**Steps of T-Test**1) Determine the type of hypothesis • Two sided**Steps of T-Test**2) Determine level of significance • Level of Significance= α**Steps of T-Test**3) Apply T-Test • Compute t- calculated (Formula) by choosing best statistical test • Compute t- tabulated…… (T- Table)**4) Make an inference…..**Reject H0 if t cal >t α/2 Reject H0 if t cal < -t α /2 Reject H0 if t cal >t α Reject H0 if t cal < -t α Steps of T-Test**Steps of T-Test**5) Conclusion • Accept or reject H0**One sample T-test**To compare population mean with sample mean**One sample T-Test**df = n-1**Example**• The average Hb level of normal woman is 13. The doctor at clinic A feels that the pregnant women coming at clinic are mostly anemic. She takes a random sample of 25 pregnant women and looks at their Hb. The data is given below • Sample mean X=11.8 • Sample SD s=2.6 • Sample size n=25 • Level of significance α = 0.05 Hypothesis ???**Example**• 1) H0= µ>13 Ha= µ<13 • 2) α = 0.05 • 3) t cal= -2.32 T tabulated(0.05’24)= -1.711**Example**4) Reject H0 if t cal < -t tab • Hence t cal < -1.711 5) Conclusion • Therefore we reject H0 at 5% significance level. • Average Hb of pregnant women at clinic A is less than that of normal women**Two Independent Samples t-test**• For comparison of two means • To compare one group with other**Example**Null Hypothesis (Ho): H1 = H2 Alternative hypothesis (Ha): H1 = H2 α = 0.05**T- tabulated**• α = 0.05 • D.F= n1+n2-2 60+52-2= 110 • Look into T- Table • T tabulated= 1.98**Inference**• T calculated=3.6 > t tabulated=1.98 Conclusion ???**Independent sample t-test to compare mean age of males and**females**Contd…**What’s your interpretation?**Independent sample t-test comparing mean weight of males and**females**Contd..**What’s your interpretation?

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