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Hypothesis_Testing_for_the_Difference_between_Two_Population_Means

Hypothesis_Testing_for_the_Difference_between_Two_Population_Means

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Hypothesis Testing for the Difference between two Population Means Prof. M.Vaisfeld Apr 25'10 if the null hypothesis will be rejected as result of testing usually should be placed (see handouts # 15, 15a and the illustrative Fig. 7.3.1 on pg. 236 ) 7.3.1 Researchers wish to know if the data they have collected provide sufficient evidence syndrome and normal individuals. The data consists of serum uric acid readings on 12 individuals with Down's syndrome and 15 normal individuals. The sample means are for the Down's syndrome population and 1.5 for the normal population. Let α = 0.05. SAMPLE 1 12 4.5 1 HYPOTHESES SAMPLE 2 15 0 Null hypothesis 3.4 1.5 0 Alternative hypothesis 0 0.05 -1.95996 <== critical value at of the curve f(z) 1.959964 <== critical value at Test statistic of the curve f(z) 2.277216 2.277216 > 1.959964 0.023 LESS than α ################################################################################## (see handouts # 15, 15a) 7.3.1A Researchers wish to know if the data they have collected provide sufficient evidence on 12 individuals with Down's syndrome and 15 normal individuals. The sample means are for the Down's syndrome population and 1.5 for the normal population. Let α = 0.05. SAMPLE 1 12 4.5 1 HYPOTHESES SAMPLE 2 15 1.7 Null hypothesis 3.4 1.2247449 1.7 Alternative hypothesis 1.7 0.05 -1.64485 <== critical value at of the curve f(z) Test statistic -1.4013 FAIL TO -1.4013 > -1.644854 0.0806 GREATER than α ###################################################################################### (see handouts # 15, 15a) 7.3.1A Researchers wish to know if the data they have collected provide sufficient evidence readings on 12 individuals with Down's syndrome and 15 normal individuals. The sample is equal to 1 for the Down's syndrome population and 1.5 for the normal population. Let α = 0.05. SAMPLE 1 12 4.5 1 HYPOTHESES SAMPLE 2 15 -1 Null hypothesis 3.4 1.2247449 -1 Alternative hypothesis -1 0.05 1.644854 <== critical value is of the curve f(z) Test statistic 4.904543 4.904543 > 1.644854 0.0000 LESS than α (sheet 1 ) Sampling from Two Normally Distributed Populations: Population Variances σ 1 2 and σ 2 2 are known, or they are unknown but both sample sizes n 1 and n 2 are greater than 30. z statistic is used within the sheet 1. Solving the problems remember that what we hope or expect to be able to conclude in the alternative hypothesis H A . Formulate at first the alternative hypothesis H A and only then the null hypothesis H 0 which should be complementary to H A . Then find a block of cells that corresponds to your hypotheses H 0 and H A and enter the data only in the data entry cells (of that block) belonging to B -column. TWO-Sided Hypothesis Test of type of the Example 7.3.1 on pg. 235 of Biostatistics book H 0 : µ 1 – µ 2 = (µ 1 – µ 2 ) 0 , H A : µ 1 – µ 2 ≠ (µ 1 – µ 2 ) 0 to indicate a difference in mean serum uric acid levels between individuals with Down's x mean_1 * = 4.5 mg/100 ml and x mean_2 * = 3.4 mg/100 ml, respectively. A variance is equal to 1 Size n 1 = The mean x mean_1 * = Standard deviation σ 1 or s 1 = Size n 2 = H 0 : µ 1 – µ 2 = The mean x mean_2 * = Standard deviation σ 2 or s 2 = H A : µ 1 – µ 2
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