# Final Review Answers. Two-Tailed t Test Solution -1 H 0 : H a :  = df = Critical Value(s): Test Statistic: Decision:  = 368   368.05 25 - 1 = 24 t.

## Presentation on theme: "Final Review Answers. Two-Tailed t Test Solution -1 H 0 : H a :  = df = Critical Value(s): Test Statistic: Decision:  = 368   368.05 25 - 1 = 24 t."— Presentation transcript:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Reject at  =.01

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

Reject at  =.05

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

Reject at  =.05

 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

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

Reject at  =.05

 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

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

Reject at  =.05

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