# (F1-F₂) - do √ot/m₂ +03/m₂ σε and σε known A random sample of size n₁ = 25, taken from a normal population with a standard deviation d = 5, has a mean x = 80. A second random sample of size 1₂ = 36, taken from a different normal population with a standard deviation o₂ = 3, has a mean x2 = 75. Using 5% level of significance, check whether #₁ > H2 H1-H2= do Reject Ho: ₂₂ n 2= (7-2)-do p/1/₁+1/₂ e=₁+n₂-2. ay but unknown. (₂-1)+(₂-1) A₁+B₂-2 The following data represent the length of time, in days, to recovery for patients randomly treated with one of two medications to clear up severe bladder infections: P1-1₂= do Medication 1 14 17 1.5 Medication 2 16 19 1.8 $² Using 0.01 level of significance, determine if medication 1 is more effective in treating the infection than medication 2, assuming normal populations with equal variances Reject Ho: Medication 1 is more effective than Medication 2. z<-%a => % z <-a/2 or => ²a/2 Two kinds of thread are being compared for strength. Fifty pieces of each type of thread are tested under similar conditions. Brand A has an average tensile strength of 78.3 kilograms with a standard deviation of 5.6 kilograms, while brand B has an average tensile strength of 87.2 kilograms with a standard deviation of 6.3 kilograms. Using a=0.01, test the hypothesis that the mean strength of brand B has a higher strength than that of Brand A. #41-42 < do H1-H2> do #1-12 do Reject Ho: H> HA P1-14 do P1-P₂>do P1-17 do 16-a E> t<-1/2 or 1>la/2 An experiment reported in Popular Science compared fuel economies for two types of similarly equipped diesel mini-trucks. Let us suppose that 12 Volkswagen and 10 Toyota trucks were tested in 90-kilometer-per-hour steady- paced trials. If the 12 Volkswagen trucks averaged 16 kilometers per liter with a standard deviation of 1.0 kilometer per liter and the 10 Toyota trucks averaged 11 kilometers per liter with a standard deviation of 0.8 kilometer per liter, Using 0.05 level of significance, determine if the mean if the fuel economy of for the average kilometers per liter for these two mini-trucks are equal. Assume that the distances per liter for the truck models are approximately normally distributed with equal variances. The fuel economy of for the average kilometers per liter for these two mini-trucks are different.

# (F1-F₂) - do √ot/m₂ +03/m₂ σε and σε known A random sample of size n₁ = 25, taken from a normal population with a standard deviation d = 5, has a mean x = 80. A second random sample of size 1₂ = 36, taken from a different normal population with a standard deviation o₂ = 3, has a mean x2 = 75. Using 5% level of significance, check whether #₁ > H2 H1-H2= do Reject Ho: ₂₂ n 2= (7-2)-do p/1/₁+1/₂ e=₁+n₂-2. ay but unknown. (₂-1)+(₂-1) A₁+B₂-2 The following data represent the length of time, in days, to recovery for patients randomly treated with one of two medications to clear up severe bladder infections: P1-1₂= do Medication 1 14 17 1.5 Medication 2 16 19 1.8 $² Using 0.01 level of significance, determine if medication 1 is more effective in treating the infection than medication 2, assuming normal populations with equal variances Reject Ho: Medication 1 is more effective than Medication 2. z<-%a => % z <-a/2 or => ²a/2 Two kinds of thread are being compared for strength. Fifty pieces of each type of thread are tested under similar conditions. Brand A has an average tensile strength of 78.3 kilograms with a standard deviation of 5.6 kilograms, while brand B has an average tensile strength of 87.2 kilograms with a standard deviation of 6.3 kilograms. Using a=0.01, test the hypothesis that the mean strength of brand B has a higher strength than that of Brand A. #41-42 < do H1-H2> do #1-12 do Reject Ho: H> HA P1-14 do P1-P₂>do P1-17 do 16-a E> t<-1/2 or 1>la/2 An experiment reported in Popular Science compared fuel economies for two types of similarly equipped diesel mini-trucks. Let us suppose that 12 Volkswagen and 10 Toyota trucks were tested in 90-kilometer-per-hour steady- paced trials. If the 12 Volkswagen trucks averaged 16 kilometers per liter with a standard deviation of 1.0 kilometer per liter and the 10 Toyota trucks averaged 11 kilometers per liter with a standard deviation of 0.8 kilometer per liter, Using 0.05 level of significance, determine if the mean if the fuel economy of for the average kilometers per liter for these two mini-trucks are equal. Assume that the distances per liter for the truck models are approximately normally distributed with equal variances. The fuel economy of for the average kilometers per liter for these two mini-trucks are different.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Transcribed Image Text:Direction: Solve the following problems in the space provided. (F1-F2)-do √0²/m₁ + 0²/m₂" 01 and 2 known H1-H2= do A random sample of size n₁ = 25, taken from a normal population with a standard deviation a₁ = 5, has a mean x = 80. A second random sample of size 1₂ = 36, taken from a different normal population with a standard deviation o₂ = 3, has a mean = 75. Using 5% level of significance, check whether ₁> H2 Reject Ho: > ₂ 2= (71-7₂)-do 5p1/n1+1/₂ v=1+0₂-2. ad but unknown, (n-1)+(₂-1) 7₁+n₂-2 The following data represent the length of time, in days, to recovery for patients randomly treated with one of two medications to clear up severe bladder infections: n X s² 1-₂ do Medication 1 14 17 1.5 Medication 2 16 19 1.8 Using 0.01 level of significance, determine if medication 1 is more effective in treating the infection than medication 2, assuming normal populations with equal variances Reject Ho: Medication 1 is more effective than Medication 2. H1-H₂ < do #1-1₂ > do #1-2 do z <-%a z > Za 2<-a/2 or 2 > ²a/2: Two kinds of thread are being compared for strength. Fifty pieces of each type of thread are tested under similar conditions. Brand A has an average tensile strength of 78.3 kilograms with a standard deviation of 5.6 kilograms, while brand B has an average tensile strength of 87.2 kilograms with a standard deviation of 6.3 kilograms. Using a-0.01, test the hypothesis that the mean strength of brand B has a higher strength than that of Brand A. Reject Ho: H> HA #1 #₂ < do #1 #₂> do #1-12 do t<-ta t>to t<-to/2 or 1>to/2 An experiment reported in Popular Science compared fuel economies for two types of similarly equipped diesel mini-trucks. Let us suppose that 12 Volkswagen and 10 Toyota trucks were tested in 90-kilometer-per-hour steady- paced trials. If the 12 Volkswagen trucks averaged 16 kilometers per liter with a standard deviation of 1.0 kilometer per liter and the 10 Toyota trucks averaged 11 kilometers per liter with a standard deviation of 0.8 kilometer per liter, Using 0.05 level of significance, determine if the mean if the fuel economy of for the average kilometers per liter for these two mini-trucks are equal. Assume that the distances per liter for the truck models are approximately normally distributed with equal variances. The fuel economy of for the average kilometers per liter for these two mini-trucks are different.

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