Exam 8: Hypothesis Testing With Two Samples

Test the claim that $\mathrm { p } _1 = \mathrm { p } _ { 2 } . \text { Use } \alpha = 0.05$ 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 the weighted estimate, $\bar { p }$ to test the claim that $\mathrm { p } _ { 1 } < \mathrm { p }_2 . \text { Use } \alpha = 0.10$ Assume the samples are random and independent. Sample statistics: $\mathrm { n } _ { 1 } = 550 , \mathrm { x } _ { 1 } = 121 , \text { and } \mathrm { n } _ { 2 } = 690 , \mathrm { x } _ { 2 } = 195$

Suppose you want to 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 $\sigma { } _ { 1 } ^ { 2 } \neq \sigma _ { 2 } ^ { 2 }$ At a Level of significance of α $\alpha$ = 0.01, when should you reject H₀? =25 =30 1=23 2=21 =1.5 =1.9

Find the standardized test statistic, t, to test the claim that $\mu _ { 1 } \neq \mu _ { 2 } .$ Two samples are random, independent, and come from populations that are normally distributed. The sample statistics are given below. Assume that $\sigma \sigma _ { 1 } ^ { 2 } \neq \sigma _{ 2 }^ { 2 } .$ =11 =18 1=6.9 2=7.3 =0.76 =0.51

In a random survey of 500 doctors that practice specialized medicine, 20% felt that the government should control health care. In a random sample of 800 doctors that were general practitioners, 30% felt that the government should control health care. Test the claim that there is a difference in the proportions. Use $\alpha$ = 0.10.

A study was conducted to determine if the salaries of elementary school teachers from two neighboring districts were equal. A sample of 15 teachers from each district was randomly selected. The mean from the first District was $28,900 with a standard deviation of $2300. The mean from the second district was $30,300 with a Standard deviation of $2100. Assume the samples are random, independent, and come from populations that Are normally distributed. Construct a 95% confidence interval for $\mu _ { 1 } - \mu _ { 2 }$ Assume that $\sigma _ { 1 } ^ { 2 } = \sigma _ { 2 } ^ { 2 } \text {. }$

A statistics teacher believes that students in an evening statistics class score higher than the students in a day class. The results of a special exam are shown below. Assume the two samples are random and independent. Can the teacher conclude that the evening students have a higher score? Use $\alpha = 0.01$ Day Students Evening Students =36 =41 1=75 2=78 =5.8 =6.3

Suppose you want to 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 $\sigma _ { 1 } ^ { 2 } = \sigma _ { 2 } ^ { 2 }$ At a Level of significance of α $\alpha = 0.05$ when should you reject H₀? =14 =12 =21 =22 =2.5 =2.8

Find the standardized test statistic, t, to 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 $\sigma _ { 1 } ^ { 2 } \neq \sigma _ { 2 }^ { 2 } \text {. }$ =25 =30 1=33 2=31 1=1.5 =1.9

Classify the two given samples as independent or dependent. Sample 1: The weights in pounds of 21 newborn females Sample 2: The weights in pounds of 21 newborn males

A physician claims that a personʹs diastolic blood pressure can be lowered if, instead of taking a drug, the person listens to a relaxation tape each evening. Ten subjects are randomly selected and pretested. Their blood pressures, measured in millimeters of mercury, are listed below. The 10 patients are given the tapes and told to listen to them each evening for one month. At the end of the month, their blood pressures are taken again. The data are listed below. Test the physicianʹs claim. Assume the samples are random and dependent, and the populations are normally distributed. Use $\alpha = 0.01$ Patient 1 2 3 4 5 6 7 8 9 10 Before 85 96 92 83 80 91 79 98 93 96 After 82 90 92 75 74 80 82 88 89 80

Construct a 90% 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 $\sigma _ { 1 } ^ { 2 } = \sigma { } _ { 2 } ^ { 2 }$ =10 =12 1=25 2=23 =1.5 =1.9

A womenʹs advocacy group claims that women golfers receive significantly less prize money than their male counterparts when they win first place in a professional tournament. The data listed below are the first place prize monies from male and female tournament winners. Assume the samples are random, independent, and come from populations that are normally distributed. Construct a 99% confidence interval for the difference in the means $\mu _ { 1 } - \mu _ { 2 }$ Assume the population variances are not equal. $\text { Female Golfers }$ 180,000 150,000 240,000 195,000 202,500 120,000 165,000 225,000 150,000 315,000 $\text { Male Golfers }$ 864,000 810,000 1,170,000 810,000 630,000 1,050,000 945,000 1,008,000 900,000 756,000 630,000 900,000

Find the weighted estimate, $\overline { \mathrm { p } }$ to test the claim that $\mathrm { p } _ { 1 } = \mathrm { p } _ { 2 } \text {. Use } \alpha = 0.05$ 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 the standardized test statistic to test the claim that $\mu _ { 1 } \neq \mu _ { 2 } .$ Assume the two samples are random and independent. Population statistics: $\sigma _ { 1 } = 0.76 \text { and } \sigma _ { 2 } = 0.51$ Sample statistics: $\overline { \mathrm { x } } 1 = 4.1 , \mathrm { n } _ { 1 } = 51 \text { and } \overline { \mathrm { x } } 2 = 4.5 , \mathrm { n } _ { 2 } = 38$

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. Test the claim that the test preparation had no effect on their scores. Assume the samples are random and dependent, and the populations are normally distributed. Use $\alpha =$ .05. 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

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 $\alpha = 0.05$ Sample statisticsstatistics: $\mathrm { n } = 12 , \overline { \mathrm { d } } = 6.0 , \mathrm {~s} \mathrm {~d} = 1.3$

Find the critical value, $t _ { 0 } ,$ to test the claim that $\mu _ { \mathrm { d } }$ = 0. Assume the samples are random and dependent, and the populations are normally distributed. Use $\alpha$ = 0.01. A 8.2 9.2 11.1 8.1 8.2 B 10.6 9.5 9.4 9.3 10.7

Construct a 95% confidence interval for $\mu _ { 1 } - \mu _ { 2 }$ Assume the two samples are random and independent. The sample statistics are given below. Population statistics: $\sigma _ { 1 } = 1.5 \text { and } \sigma _ { 2 } = 1.9$ Sample statistics: $\overline { \mathrm { x } } 1 = 25 , \mathrm { n } _ { 1 } = 50 \text { and } \overline { \mathrm { x } } 2 = 23 , \mathrm { n } _ { 2 } = 60$

Find the standardized test statistic to test the claim that $\mu _ { 1 } = \mu _ { 2 } .$ Assume the two samples are random and independent. Population statistics: $\sigma _ { 1 } = 1.5 \text { and } \sigma _ { 2 } = 1.9$ Sample statisticsstatistics: $\bar { x }_ 1 = 24 , \mathrm { n } _ { 1 } = 50 \text { and } \bar { x }_ 2 = 22 , n _ { 2 } = 60$