# Probability

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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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