Exam 8: Hypothesis Testing With Two Samples

Construct a 95% confidence interval for $\mathrm { p } _ { 1 } - \mathrm { p } _ { 2 }$ for a survey that finds 30% of 240 randomly selected males and 41% of 200 randomly selected females are opposed to the death penalty.

Test the claim that $\mu _ { 1 } = \mu _ { 2 } .$ Two samples are random, independent, and come from populations that are normally distributed. The sample statistics are given below. Assume that $\sigma _{ 1 } ^{ 2 } \neq \sigma _{ 2 } ^{ 2 } \text {. Use } \alpha = 0.05$ =25 =30 =18 =16 =1.5 =1.9

At α $\alpha$ = 0.05, test a financial advisorʹs claim that the difference between the mean dividend rate for listings in the NYSE market and the mean dividend rate for listings in the NASDAQ market is more than 0.75. Assume the two samples are random and independent. NYSE =30 =2.75\% =1.14\% NASDAQ =50 =1.66\% =0.63\%

Find $\overline { \mathrm { d } } .$ Assume the samples are random and dependent, and the populations are normally distributed. 13 11 30 26 14 11 7 8 18 5

Test the claim that $\mu _ { 1 } > \mu _ { 2 }$ Assume the two samples are random and independent. Use $\alpha = 0.01 .$ Population statistics: $\sigma _ { 1 } = 45 \text { and } \sigma _ { 2 } = 25$ Sample statisticsstatistics: $\overline { \mathrm { x } } 1 = 630 , \mathrm { n } _ { 1 } = 100 \text { and } \overline { \mathrm { x } } 2 = 615 , \mathrm { n } _ { 2 } = 125$

Construct a 95% confidence interval for $\mu _ { 1 } - \mu _ { 2 }$ Two samples are random, independent, and come from populations that are normally distributed The sample statistics are given below. Assume that $\sigma _ { 1 } ^ { 2 } = \sigma _ { 2 } ^ { 2 }$ =11 =18 1=4.8 2=5.2 =0.76 =0.51

A local school district is concerned about the number of school days missed by its teachers due to illness. A random sample of 10 teachers is selected. The number of days absent in one year is listed below. An incentive program is offered in an attempt to decrease the number of days absent. The number of days absent in one year after the incentive program is listed below. Test the claim that the incentive program cuts down on the number of days missed by teachers. Assume the samples are random and dependent, and the populations are normally distributed. Use $\alpha = 0.05 .$ Teacher A B C D E F G H I J Days absent before incentive 3 8 7 2 9 4 2 0 7 5 Days absent after incentive 1 7 7 0 8 2 0 1 5 5

Construct a 95% confidence interval for $p _ { 1 } - p _ { 2 }$ Assume the samples are random and independent. Sample statistics: $\mathrm { n } _ { 1 } = 50 , \mathrm { x } _ { 1 } = 35 , \text { and } \mathrm { n } _ { 2 } = 60 , \mathrm { x } _ { 2 } = 40$

Find $\mathrm { s } _ { \mathrm { d } }$ Assume the samples are random and dependent, and the populations are normally distributed. A 5.3 6.3 8.2 5.2 5.3 B 7.7 6.6 6.5 6.4 7.8

Find $\mathrm { s } _ { \mathrm { d } }$ Assume the samples are random and dependent, and the populations are normally distributed. A 27 25 44 40 28 B 25 21 22 32 19

At a local college, 65 female students were randomly selected and it was found that their mean monthly income was $616 with a population standard deviation of $121.50. Seventy-five male students were also randomly selected and their mean monthly income was found to be $658 with a population standard deviation of $168.70. Test the claim that male students have a higher monthly income than female students. Use $\alpha = 0.01$

Test the claim that the paired sample data is from a population with a mean difference of 0. Assume the samples are random and dependent, and the populations are normally distributed. Use $\alpha = 0.05 .$ A 30 28 47 43 31 B 28 24 25 35 22

Test the claim that $\mu _ { \mathrm { d } } > 0$ using the sample statistics below. Assume the samples are random and dependent, and the populations are normally distributed. Use $\alpha = 0.01$ Sample statistics: $\mathrm { n } = 15 , \overline { \mathrm { d } } = 4.0 , \mathrm {~s} \mathrm {~d} = 0.2$

Suppose you want to test the claim that $\mu _ { 1 } > \mu _ { 2 }$ Assume the two samples are random and independent. If a hypothesis test is performed, how should you interpret a decision that rejects the null hypothesis?

A local bank claims that the waiting time for its customers to be served is the lowest in the area. A competitor bank checks the waiting times at both banks. Assume the two samples are random and independent. Use $\alpha$ α = 0.05 and a confidence interval to test the local bankʹs claim. Local Bank =45 =5.3 minutes =1.1 minutes Competitor Bank =50 =5.6 minutes =1.0 minute

Find $\overline { \mathrm { d } } .$ Assume the samples are random and dependent, and the populations are normally distributed. 2.5 3.5 5.4 2.4 2.5 4.9 3.8 3.7 3.6 5.0

Test the claim that $\mu _ { 1 } < \mu _ { 2 }$ Two samples are random, independent, and come from populations that are normally distributed. The sample statistics are given below. Assume that $\sigma _ { 1 } ^ { 2 } = \sigma _ { 2 } ^ { 2 } \text {. Use } \alpha = 0.025$ =15 =15 =24.63 =27.18 =2.9 =2.8

Two groups of patients with colorectal cancer are treated with a different drug to reduce pain. A random sample of 140 patients are treated using the drug Irinotican and a random sample of 127 patients are treated using the drug Fluorouracil. Assume the two samples are random and independent. At α $\alpha$ = 0.01, test a pharmaceutical representativeʹs claim that the difference between the mean number of pain-free months for patients using Fluorouracil and the mean number of pain-free months for patients using Irinotican is less than two months. Fluorouracil =127 =8.5 months =1.5 months Irinotican =140 =10.3 months =1.2 months

Nine students took the SAT. Their scores are listed below. Later on, they took a test preparation course and retook the SAT. Their new scores are listed below. Construct a 95% confidence interval for $\mu _ { \mathrm { d } }$ Assume the Samples are random and dependent, and the populations are normally distributed. Student 1 2 3 4 5 6 7 8 9 Scores before course 720 860 850 880 860 710 850 1200 950 Scores after course 740 860 840 920 890 720 840 1240 970

Construct a 99% confidence interval for data sets A and B. Data sets A and B are random and dependent, and the populations are normally distributed. Round to the nearest tenth. A 5.8 6.8 8.7 5.7 5.8 B 8.2 7.1 7.0 6.9 8.3