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Final Review Answers

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Two-Tailed t Test Solution -1 H 0 : H a : = df = Critical Value(s): Test Statistic: Decision: = 368 368.05 25 - 1 = 24 t 02.064-2.064.025 Reject H 0 0.025 Reject at =.05 P-value = 0

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Two-Tailed Z Test Solution -2 H 0 : H a : = n = Critical Value(s): Test Statistic: Decision: = 70 70.05 36 Z 01.96-1.96.025 Reject H 0 0.025 Do not reject at =.05

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One-Tailed Z Test Solution -3 H 0 : H a : = n = Critical Value(s): Test Statistic: Decision: = 32 < 32.01 60 Z 0-2.33.01 Reject Reject at =.01

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Two-Tailed t Test Solution-4 H 0 : H a : df Critical Value(s): Test Statistic: Decision: = 3.25 3.25.01 64 - 1 = 63 t 02.656-2.656.005 Reject H 0 0.005 Do not reject at =.01

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One-Tailed t Test Solution - 5 H 0 : H a : = df = Critical Value(s): Test Statistic: Decision: = 140 < 140.05 20 - 1 = 19 t 0-1.729.05 Reject H 0 Reject at =.05

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One-Tailed t Test Solution -6 H 0 : H a : = df = Critical Value(s): Test Statistic: Decision: = 5 < 5.05 10 - 1 = 9 t 01.833.05 Reject H 0 Do not reject at =.05

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One-Proportion Z Test Solution - 7 H 0 : H a : = n = Critical Value(s): Test Statistic: Decision: p =.10 p <.10.05 200 Z 0-1.645.05 Reject H 0 Reject at =.05

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One-Proportion Z Test Solution - 8 H 0 : H a : = n = Critical Value(s): Test Statistic: Decision: p =.04 p .04.05 500 Z 01.96-1.96.025 Reject H 0 0.025 Do not reject at =.05

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1.Miles per gallon ratings of cars before and after mounting radial tires - DEPENDENT 2.The life expectancy of light bulbs made in two different factories - INDEPENDENT 3.Difference in hardness between two metals: one contains an alloy, one doesn’t - INDEPENDENT 4.Tread life of two different motorcycle tires: one on the front, the other on the back - DEPENDENT 9

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H 0 : H a : df Critical Value(s): 1 - 2 = 0 ( 1 = 2 ) 1 - 2 0 ( 1 2 ).05 11 -1 = 10 t 02.228-2.228.025 Reject H 0 0.025 Small-Sample Test Solution 10-A Test Statistic: Do not reject at =.05

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H 0 : H a : df Critical Value(s): 1 - 2 = 1% ( 1 = 2 ) 1 - 2 1% ( 1 2 ).05 11 -1= 10 Small-Sample Test Solution 10-B Test Statistic: Do not reject at =.05 t 0-1.812.05 Reject H 0

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Large-Sample Test Solution - 11 H 0 : H a : n 1 =, n 2 = Critical Value(s): t 0 1.761-1.761.05 Reject H 0 0.05 1 - 2 = 0 ( 1 = 2 ) 1 - 2 0 ( 1 2 ).10 15 15 Do not reject at =.10

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Paired-Difference Solution-12 H 0 : H a : = df = Critical Value(s): d = 0 ( d = A - B ) d < 0.10 4 - 1 = 3 t 0-1.638.10 Reject H 0

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Computation Table ObservationBeforeAfterDifference Sam85949 Tamika9487 -7 Brian78791 Mike87881 Total4 d = 1S d = 6.53

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Test Statistic: Decision: Do not reject at =.10

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H 0 : H a : = n 1 = n 2 = Critical Value(s): p 1 - p 2 = 0 p 1 - p 2 0.01 7882 z 0 2.58-2.58 Reject H 0 0.005 Test for Two Proportions Solution -13

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Reject at =.01

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H 0 : H a : = n MA = n CA = Critical Value(s): p MA – p CA = 0 p MA – p CA < 0.05 1500 Z 0-1.645.05 Reject H 0 Test for Two Proportions Solution - 14

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Reject at =.05

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H0: Ha: = n 1 = n 2 = n 3 = Critical Value(s): p 1 = p 2 = p 3 = 1/3 At least 1 is different.05 634572 =.05 2 0 Reject H 0 5.991 2 Test for k Proportions Solution - 15

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Reject at =.05

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2 Test of Independence Solution - 16 H 0 : H a : = df = Critical Value(s): No Relationship Relationship.05 (2 - 1)(2 - 1) = 1 2 0 Reject H 0 3.841 =.05

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112·82 160 48·78 160 48·82 160 112·78 160

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Reject at =.05

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2 Test of Independence Solution -17 H 0 : H a : = df = Critical Value(s): No Relationship Relationship.05 (2 - 1)(2 - 1) = 1 2 0 Reject H 0 3.841 =.05

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170·132 286 170·154 286 116·132 286 154·132 286

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Reject at =.05

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The t-distribution William Gosset lived from 1876 to 1937 Gosset invented the t -test to handle small samples for quality control in brewing. He wrote.

The t-distribution William Gosset lived from 1876 to 1937 Gosset invented the t -test to handle small samples for quality control in brewing. He wrote.

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