Question

1. Forty refrigerators from two different models of a refrigerator manufacturer are compared to see if the smaller model uses less energy than the larger model. The energy was measured in kilowatt hours per month (kwh/mo). From years of testing these models, it is known that the standard deviation of kwh/mo is 34 kwh/mo for the smaller model and 40 kwh/mo for the larger one. From this survey, the sample means and standard deviations are 125 and 34, and 90 and 40, respectively. If we conduct a hypothesis test, the decision and conclusion are Group of answer choices

a.Reject the null hypothesis and conclude that the average kwh/mo are different.

b. Do not reject the null hypothesis and conclude that the average kwh/mo are the same.

c. Do not reject the null hypothesis and conclude that the average kwh/mo for the smaller refrigerator is higher than for the larger model.

d. Reject the null hypothesis and conclude that the average kwh/mo for the smaller refrigerator is higher than for the larger model.

2.Fifty refrigerators from two different models of a refrigerator manufacturer are compared to see if the smaller model uses less energy than the larger model. The energy was measured in kilowatt hours per month (kwh/mo). From years of testing these models, it is known that the standard deviation of kwh/mo is 2.6 kwh/mo for the smaller model and 3.0 kwh/mo for the larger one. From this survey, the sample means and standard deviations are 105 and 2.4, and 119 and 3.2, respectively. The hypothesis test to use is Group of answer choices

a. independent group means, population standard deviations unknown

b. independent group means, population standard deviations known

c. matched or paired samples

d. two proportions

Answer 1

2

C35 B 1 2. 34 40 68.9 Smaller model Larger model 4 5 1) n1=n2 40 xlbar- 125 s1 x2bar 90 s2 x1bar-x2bar 35 Var(x1B-X2B) a) Ho: p1=u2 Vs Ha: u1>u2 Since the samples are independent & large. Test statistic: Under Ho, (x1bar-x2bar) Z V(s1?/n1) +(s2/n2) 6 7 8 9 10 12 13 ZE 4.216561445 pvalue= 1.24028E-05 z crit 1.644853627 Reject the null hypothesis and conclude that the average kwh/mo for the smaller refrigerator is higher than for the larger model. 14 15 16 2) 50 n1=n2= Xlbar= 105 2.4 17 s1= Smaller model Sheet1 Sheet2 sample&CI Wilcox Sheet3 testing mean Ready

B 16 17 18 0.3152 19 20 21 22 23 24 25 26 x2bar- 119 s2= 3.2 Larger model x1bar-x2bar -14 Var(x1B-X2B) 0.32 01= 2.6 02= 3 Var(u1-12) a) Ho: p1=u2 Vs Ha: u1>u2 Since the samples are independent & large. Test statistic: Under Ho, (x1bar-x2bar) Z= V(s1°/n1) +(52°/n2) case i) when population standard deviations unknown. Za 24.74873734 pvalue= 0 z crit: 1.644853627 Reject the null hypothesis and conclude that , smaller refrigerator uses less energy than for larger model. case ii) when population standard deviations known. Z= 24.9364675 pvalue= 0 z crit= 1.644853627 Reject the null hypothesis and conclude that, smaller refrigerator uses less energy than for larger model. Sheet1 Sheet2 sample&OI Wilcox Sheet3 testing mean 27 28 29 30 31 32