# T 06402 p 05351 x 03583 x σ n 1 19388 n 12 solution

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Chapter 4 / Exercise 46
Intermediate Algebra Within Reach
Larson Expert Verified
0 t = -0.6402 p = 0.5351 x = -0.3583 X σ n-1 = 1.9388 n = 12 Solution Critical value: At 1% level of significance, t crit = t 0.01/2, 12-1 = - 3.11 12 9388 . 1 35833 . 0 t calc Before we state the test statistics, we use the calculator to obtain the values: 1-Sample tTest μ 0 t = -0.6402 p = 0.5351 x = -0.3583 X σ n-1 = 1.9388 n = 12 = -0.6402 Let μ 1 =average time (mins) for oil and filter change by Procedure A Let μ 2 =average time (mins) for oil and filter change by Procedure B Condition: Normal and equal std dev but unknown Ho: D = 0 (where D = 1 - 2 ) – There is no diff in the means of two related pop or the population mean difference D is 0. Ha: D 0 (or Ho: D 1 - 2 ) ) – the population difference D is not 0 Define rejection/non-rejection regions Area= α /2=0.025 t crit = -3.11 t crit =3.11 Area= α /2=0.025 Z t calc =-0.640 Reject Ho Reject Ho Do Not Reject Ho Decision Area= α /2=0.025 t crit = -3.11 t crit =3.11 Area= α /2=0.025 Z tcalc=-0.640 Reject Ho Reject Ho Do Not Reject Ho Decision: Do not reject Ho The statistical evidence does not indicate that we may conclude there is a difference in the average times for an oil and filter change. Hypothesis Test One Population Hypothesis Test Two Populations Sample Independent Sample dependent Equal 2 ? unequal 2 1 and 2 known? Z-test Pooled Variance t-test 2 MEANS 2 Proportions Check the 4 conditions If yes Z-test Paired t-test Normal? Yes No STOP No Yes Yes No T-test Pooled variance Z-test of two Proportions Hypothesis test for Differences - Proportions for c Independent Groups – א 2 test
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Chapter 4 / Exercise 46
Intermediate Algebra Within Reach
Larson Expert Verified
1/31/2012 7 The seven-step Method of Hypothesis Testing Steps: 1.Define the parameters: π1and π22.State the hypothesis 3. Determine the appropriate test (refer to the flowchart) 4. State the conditions/assumptions: n 1 p 1 5; n 1 (p 1 -1) 5 and n 2 p 2 5; n 2 (p 2 -1) 5 5. Determine the critical value that divide the rejection and non-rejection regio 6. Calculate the test statistics value 7 Make the statistical decision and Managerial conclusion To reject Ho or DO NOT reject Ho Compare the test statistics with the critical value (critical value approach) or compare p-value with α (p-value approach) Hypothesis Test: Two Proportions (Z test for the differences in Proportions for 2 independent Groups) For a two tailed hypothesis test: 5 ) p 1 ( n , 5 p n 1 1 1 1 5 ) p 1 ( n , 5 p n 2 2 2 2 2 1 o π π : H 2 1 a π π : H Are the four conditions satisfied? Let π 2 = the population proportion of successes in group 2 Let π 1 = the population proportion of successes in group 1 See page 484, section 11.3 Hypothesis Test: Two Proportions (Z test for the differences in Proportions for 2 independent Groups) Test statistics: ) n 1 n 1 )( p 1 ( p ) π π ( ) p p ( z 2 1 2 1 2 1 2 1 2 2 1 1 2 1 2 1 n n p n p n n n x x p Where usually Л 1 Л 2 =0 since we hypothesis that Л 1= Л 2 Where p is called the pooled estimate of the population proportion Illustrative Example Two printers are tested using the same paper and graphic output. The results are then judged as conforming or nonconforming. The results follow. Test for a difference in proportion of nonconforming pages. Use 5% level of significance.
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