Exam 8: Hypothesis Testing With Two Samples

Find the standardized test statistic to test the claim that $\mu _ { 1 } = \mu _ { 2 }$ . Assume the two samples are random and independent. Population statistics: $\sigma _ { 1 } = 2.5 \text { and } \sigma _ { 2 } = 2.8$ Sample statistics: $\overline { \mathrm { x } } 1 = 3 , \mathrm { n } _ { 1 } = 40 \text { and } \overline { \mathrm { x } } 2 = 4 , \mathrm { n } _ { 2 } = 35$

A sports analyst claims that the mean batting average for teams in the American League is not equal to the mean batting average for teams in the National League because a pitcher does not bat in the American League. The data listed below are random, independent, and come from populations that are normally distributed. Construct a 95% confidence interval for the difference in the means $\mu _ { 1 } - \mu _ { 2 } .$ Assume the population variances are equal. $\text { American League }$ 0.279 0.274 0.271 0.268 0.265 0.254 0.240 $\text { National League }$ 0.284 0.267 0.266 0.263 0.261 0.259 0.256

Construct a 95% 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. 30 28 47 43 31 28 24 25 35 22 2

Construct a 98% confidence interval for $\mathrm { p } _ { 1 } - \mathrm { p } _2$ Assume the samples are random and independent. Sample statistics: $\mathrm { n } _ { 1 } = 1000 , \mathrm { x } _ { 1 } = 250 , \text { and } \mathrm { n } _ { 2 } = 1200 , \mathrm { x } _ { 2 } = 195$

A random sample of 100 students at a high school was asked whether they would ask their father or mother for help with a homework assignment in science. A second random sample of 100 different students was asked the Same question for an assignment in history. Forty-three students in the first sample and 47 students in the Second sample replied that they turned to their mother rather than their father for help. Construct a 98% Confidence interval for $\mathrm { p } _ { 1 } - \mathrm { p } _ { 2 }$

Test the claim that $\mathrm { p } _ { 1 } > \mathrm { p } _ { 2 } . \text { Use } \alpha = 0.01$ Assume the samples are random and independent. Sample statistics: $\mathrm { n } _ { 1 } = 100 , \mathrm { x } _ { 1 } = 38 , \text { and } \mathrm { n } _ { 2 } = 140 , \mathrm { x } _ { 2 } = 50$

Find the critical valuevalue, $t _ { 0 }$ to test the claim that $\mu _ { 1 } < \mu _ { 2 } .$ Two samples are random, independent, and come from populations that are normal. The sample statistics are given below. Assume that $\sigma { } _ { 1 } ^ { 2 } = \sigma _ { 2 } ^{ 2 } \text {. Use } \alpha = 0.05$ =15 =22.2 =2.9 =15 =24.75 =2.8

A recent survey showed that in a random sample of 100 elementary school teachers, 15 smoked. In a random sample of 180 high school teachers, 36 smoked. Is the proportion of high school teachers who smoke greater than the proportion of elementary teachers who smoke? Use $\alpha = 0.01$

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 $\alpha$ = 0.05. A 19 17 36 32 20 B 17 13 14 24 11

In a study of effectiveness of physical exercise on weight loss, 20 people were randomly selected to participate in a program for 30 days. Test the claim that exercise had no bearing on weight loss. Assume the samples are random and dependent, and the populations are normally distributed. Use $\alpha = 0.02 .$ Weight before Program 178 210 156 188 193 225 190 165 168 200 (in pounds) Weight after Program 182 205 156 190 183 220 195 155 165 200 (in pounds) Weight before Program 186 1725 166 184 225 145 208 214 148 174 (in pounds) Con't Weight after Program 180 173 165 186 240 138 203 203 142 174 (in pounds) Con't

Find the critical value, $t _ { 0 }$ to test the claim that $\mu _ { 1 } > \mu _ { 2 } .$ Two samples are random, independent, and come from populations that are normal. The sample statistics are given below. Assume that $\sigma { } _ { 1 } ^ { 2 } \neq \sigma _ { 2 }^ { 2 }$ Use α = 0.01. =18 =13 1=600 =585 =40 =25

Classify the two given samples as independent or dependent. Sample 1: The scores of 22 students who took the ACT Sample 2: The scores of 22 different students who took the SAT

Test the claim that μd < 0 using the sample statistics below. Assume the samples are random and dependent, and the populations are normally distributed. Use α = 0.10. Sample statistics: $\mathrm { n } = 18 , \overline { \mathrm { d } } = - 1.5 , \mathrm {~s} \mathrm {~d} = 0.2$

Test the claim that $\mathrm { p } _ { 1 } \neq \mathrm { p } _ { 2 } . \text { Use } \alpha = 0.02$ Assume the samples are random and independent. Sample statistics: $\mathrm { n } _ { 1 } = 1000 , \mathrm { x } _ { 1 } = 250 \text {, and } \mathrm { n } _ { 2 } = 1200 , \mathrm { x } _ { 2 } = 195$

Find the weighted estimate, $\overline { \mathrm { p } }$ tto test the claim that $\mathrm { p } _ { 1 } \neq \mathrm { p } _ { 2 } \text {. Use } \alpha = 0.02$ Assume the samples are random and independent. Sample statistics: $\mathrm { n } _ { 1 } = 1000 , \mathrm { x } _ { 1 } = 250 \text {, and } \mathrm { n } _ { 2 } = 1200 , \mathrm { x } _ { 2 } = 195$

Test the claim that $\mu _ { 1 } = \mu _ { 2 }$ Assume the two samples are random and independent. Use $\alpha$ = 0.05. Population statistics: $\sigma _ { 1 } = 1.5 \text { and } \sigma _ { 2 } = 1.9$ Sample statisticsstatistics: $\overline { \mathrm { x } } 1 = 17 , \mathrm { n } _ { 1 } = 50 \text { and } \overline { \mathrm { x } } 2 = 15 , \mathrm { n } _ { 2 } = 60$

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. At α $\alpha$ = 0.01, test the groupʹs claim. 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

A study was conducted to determine if the salaries of elementary school teachers from two neighboring states were equal. A sample of 100 teachers from each state was randomly selected. The mean from the first state was $29,100 with a population standard deviation of $2300. The mean from the second state was $30,500 with a population standard deviation of $2100. Test the claim that the salaries from both states are equal. Use $\alpha = 0.05$

Classify the two given samples as independent or dependent. Sample 1: Pre-training weights of 18 people Sample 2: Post-training weights of 18 people

As part of a Masterʹs thesis project, a mathematics teacher is interested in the effects of two different teaching methods on mathematics achievement. She randomly chooses one class of students to learn an algebraic Concept using traditional methods and another class of students to learn the same algebraic concept using Manipulatives. The teacher then compares their test scores. Determine whether the samples are dependent or Independent.