T- Test

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T- Test

• Prof. Dr. Ramez Bedwany

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Comparison of two independent samplest- Test

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

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• pooled Variance

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• Critical t from table at degree of freedom
• n1 n2-2
• If n1 n2 lt 120 use t test
• If n1 n2 120 use z test with the same formula

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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

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Answer

• n125 X1125 S110
• n217 X2132 S212
• df n1n2-2 2517-240
• Critical t at 40, 1 level of significance 2.704

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• 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

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Exercise

• Example 2 and 3

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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

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• di difference (after-before)
• Sd standard deviation of difference
• n sample size
• Critical t from table at df n-1

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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

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• Serial number
  BP BP
• 
  Before
  after
•  
• I
  200
  180
• 2
  160
  165
• 3
  190
  175
• 4
  185
  185
• 5
  210
  170
• 6
  175
  160

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ANSWER
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• -14.17
• 
  15.942

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• Critical t at df6-15 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
•  

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Assignment

???? ???? ???? ???? ???? ???? ????? ???? ???? ??? ???? ??? ???? Measures of Dispersion
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Outcomes

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