# Reject h if the p value is less than α in the trash

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Chapter 1 / Exercise 5
Mathematics: A Practical Odyssey
Johnson/Mowry
Expert Verified
Reject H 0 if the p-value is less than α In the trash bag case, α was set to 0.05 The calculated p-value of 0.0139 is < α = 0.05 This implies that the test statistic z = 2.20 is greater than the rejection point z 0.05 = 1.645 Therefore reject H 0 at the α = 0.05 significance level LO9-3
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Chapter 1 / Exercise 5
Mathematics: A Practical Odyssey
Johnson/Mowry
Expert Verified
9-40 Steps in Testing a “Less Than” Alternative in Payment Time Case #1 1. State the null and alternative hypotheses In the payment time case, H 0 : 19.5 vs. H a : < 19.5, where is the mean bill payment time (in days) 2. Specify the significance level α In the payment time case, set α = 0.01 3. Select the test statistic In the payment time case, use the test statistic A negative value of this this test statistic results from a sample mean that is less than 19.5 days n . x . x z x 5 19 5 19 LO9-3
9-41 Steps in Testing a “Less Than” Alternative in Payment Time Case #2 4. Determine the critical value rule Decide how much less than 0 test statistic must be to reject H 0 with probability of α The probability α is the area in the left-hand tail of the standard normal curve Use standard normal table to find the rejection point z α Since α = 0.01 in the payment time case, the rejection point is z α = z 0.01 = 2.33 Reject H 0 in favor of H a if the test statistic z is calculated to be less than the rejection point z α In the payment time case, reject H 0 if the test statistic z is less than 2.33 LO9-3
9-42 Steps in Testing a “Less Than” Alternative in Payment Time Case #3 5. Collect the sample data and calculate the value of the test statistic In the payment time case, assume that σ is known and σ = 4.2 days For a sample of n=65, = 18.1077 days: 67 2 65 2 4 5 19 1077 18 5 19 . . . . n . x z LO9-3
9-43 Steps in Testing a “Less Than” Alternative in Payment Time Case #4 6. Decide whether to reject H 0 by using the test statistic and the rejection rule Compare the value of the test statistic to the rejection point according to the rejection rule In the payment time case, z = 2.67 is less than z 0.01 = - 2.33 Therefore reject H 0 : μ ≥ 19.5 in favor of H a : μ < 19.5 at the 0.01 significance level 7. Interpret the statistical results in managerial terms and assess their practical importance Can conclude that the mean bill payment time of the new billing system is less than 19.5 days LO9-3
9-44 Steps Using a p- value to Test a “Less Than” Alternative (Steps 1 3 are the same) 4. Collect the sample data and compute the value of the test statistic In the payment time case, the value of the test statistic was calculated to be z = 2.67 5. Calculate the p-value by corresponding to the test statistic value In the payment time case, the area under the standard normal curve in the left-hand tail to the left of the test statistic z = 2.67 The area is = 0.0038 The p-value is 0.0038 LO9-3
9-45 Steps Using a p- value to Test a “Less Than” Alternative Continued 5.