Probability Essay, Research Paper
Problem 6.15
Test: one-tailed z test for value of population mean
Null Hypothesis: H0: population mean = 16
Alternative Hypothesis: Ha : population mean * 16
Standard Error: 9.32 / sq.rt. (33) = 1.62
Test Statistic: (9 – 16) / 1.62 = -4.32
Critical Value for z, alpha= 0.10 = 1.28
Acceptance Region from -1.28 to + infinity
Reject the null hypothesis
Problem 6.21
Test: one-tailed z test for value of population mean
Null Hypothesis: H0: population mean = 1502.5
Alternative Hypothesis: Ha : population mean * 1502.5
Standard Error: 97.3 / sq.rt. (225) = 6.49
Test Statistic: (1511.4 – 1502.5) / 6.49 = 1.37
Critical Value for z, alpha= 0.05 = 1.645
Acceptance Region from negative infinity to + 1.645
Do NOT reject null hypothesis.
Problem 6.49
Test: one-tailed t test (n * 30) for value of population mean
Null Hypothesis: H0: population mean = 15
Alternative Hypothesis: Ha : population mean * 15
Standard Error: 5.4 / sq.rt. (12) = 1.56
Test Statistic: (12.3-15) / 1.56 = -1.73
Critical Value for z, alpha= 0.05 = 1.645
Acceptance Region from -1.645 to + infinity
Reject the null hypothesis
Problem 6.59
Test: one-tailed z test for value of population proportion
Null Hypothesis: H0: population proportion = 0.4
Alternative Hypothesis: Ha : population proportion * 0.4
Standard Error: sq.rt. (0.4*0.6/337) = 0.027
Sample proportion = 133/337 = 0.395
Test Statistic: (0.395 – 0.400) / 0.027 = -0.19
Critical Value for z, alpha= 0.10 = 1.28
Acceptance Region from -1.28 to + infinity
Do NOT reject the null hypothesis
Problem 7.15
Test: one-tailed z test for difference between two population means
Null Hypothesis: H0: mean1 – mean2 = 0
Alternative Hypothesis: Ha : mean1 – mean2 * 0
Standard Error: sq.rt. (7.37?/44 + 16.09?/44) = 2.78
Test Statistic: [(7.295-14.666) - 0] / 2.78 = -2.65
Critical Value for z, alpha= 0.05 = 1.645
Acceptance Region from -1.645 to + infinity
Reject the null hypothesis
Problem 8.13
Test: two-tailed z test for difference between two population proportions
Null Hypothesis: H0: p1 – p2 = 0
Alternative Hypothesis: Ha : p1 – p2 not equal to 0
p1 = 35/100 = 0.35; p2 = 9/96 = 0.09 p = 44/196 = .22
Standard Error: sq.rt. (.22*.78 *(1/100 + 1/96)) = 0.059
Test Statistic: [(.35 - .09) - 0] / 0.059 = 4.41
Critical Value for z, alpha= 0.05 = 1.96
Acceptance Region from -1.96 to + 1.96
Reject the null hypothesis
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