Exam 8: Hypothesis Testing With Two Samples

A researcher wishes to determine whether people with high blood pressure can lower their blood pressure by following a certain diet. A treatment group and a control group are selected. Assume the two samples are random and independent. Construct a 90% confidence interval for the difference between the two population means, $\mu _ { 1 } - \mu _ { 2 } .$ Would you recommend using this diet plan? Explain your reasoning. Treatment Group =100 1=178 =35 Control Group =100 =193 =37

Find the standardized test statistic to test the claim that $\mu _ { 1 } < \mu _ { 2 }$ Assume the two samples are random and independent. Population statistics: $\sigma _ { 1 } = 2.9 \text { and } \sigma _ { 2 } = 2.8$ Sample statisticsstatistics: $\overline { \mathrm { x } } 1 = 20.16 , \mathrm { n } _ { 1 } = 35 \text { and } \overline { \mathrm { x } } 2 = 22.71 , \mathrm { n } _ { 2 } = 42$

Find the critical value, $t _ { 0 }$ to test the claim that $\mu _ { 1 } \neq \mu _ { 2 } .$ Two samples are random, independent, and come from populations that are normal. The sample statistics are given below. Assume that $\sigma \sigma _ { 1 } ^ { 2 } \neq \sigma _ { 2 } ^{ 2 } \text {. Use } \alpha = 0.02$ =11 =18 1=3.9 =4.3 =0.76 =0.51

In a recent survey of gun control laws, a random sample of 1000 women showed that 65% were in favor of stricter gun control laws. In a random sample of 1000 men, 60% favored stricter gun control laws. Test the claim that the percentage of men and women favoring stricter gun control laws is the same. Use $\alpha = 0.05$

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

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 $\alpha$ = 0.02. 8 9.2 11.1 8.1 8.2 B 5.4 4.3 5.2 4.1 5.5

To test the effectiveness of a new drug designed to relieve pain, 200 patients were randomly selected and divided into two equal groups. One group of 100 patients was given a pill containing the drug while the other group of 100 was given a placebo. What can we conclude about the effectiveness of the drug if 62 of those actually taking the drug felt a beneficial effect while 41 of the patients taking the placebo felt a beneficial effect? Use $\alpha$ = 0.05.

Find the critical values, $\mathrm { t } _ { 0 } ,$ 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 $\sigma _ { 1 } ^ { 2 } \neq \sigma _ { 2 } ^ { 2 } \text {. }$ Use $\alpha$ = 0.05. =25 1=17 =1.5 =30 =15 =1.9

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 $\alpha = 0.01$ A 5.6 6.6 8.5 5.5 5.6 B 8.0 6.9 6.8 6.7 8.1

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 sample of 100 different students was asked the same question for an assignment in history. If 43 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, test the claim whether the difference between the proportions is due to chance. Use α = 0.02.

Find the standardized test statistic estimate, z, to test the claim that $\mathrm { p } _1 > \mathrm { p } _ { 2 }$ Assume the samples are random and independent. Sample statistics: $\mathrm { n } _ { 1 } = 100 , \mathrm { x } _ { 1 } = 38 , \text { and } \mathrm { n } _ { 2 } = 140 , \mathrm { x } _ { 2 } = 50$

A recent study of 100 elementary school teachers in a southern state found that their mean salary was $24,700 with a population standard deviation of $2100. A similar study of 100 elementary school teachers in a western state found that their mean salary was $35,100 with a population standard deviation of $3200. Test the claim that the salaries of elementary school teachers in the western state is more than $10,000 greater than that of elementary teachers in the southern state. Use $\alpha$ = 0.05. Assume the two samples are random and independent.

Test the claim that $\mathrm { p } _ { 1 } < \mathrm { p } _ { 2 } . \text { Use } \alpha = 0.10$ AssumAssume the samples are random and independent. Sample statistics: $\mathrm { n } _ { 1 } = 550 , \mathrm { x } _ { 1 } = 121 \text {, and } \mathrm { n } _ { 2 } = 690 , \mathrm { x } _ { 2 } = 195$

Find the standardized test statistic, z to test the claim that $\mathrm { p } _ { 1 } = \mathrm { p } _ { 2 }$ Assume the samples are random and independent. Sample statistics: $\mathrm { n } _ { 1 } = 50 , \mathrm { x } _ { 1 } = 35 , \text { and } \mathrm { n } _ { 2 } = 60 , \mathrm { x } _ { 2 } = 40$

Test the claim thathat $\mu _ { 1 } \neq \mu _ { 2 }$ Assume the two samples are random and independent. Use $\alpha = 0.02$ Population statistics: $\sigma _ { 1 } = 0.76 \text { and } \sigma _ { 2 } = 0.51$ Sample statistics: $\overline { \mathrm { x } } 1 = 5.3 , \mathrm { n } _ { 1 } = 51 \text { and } \overline { \mathrm { x } } 2 = 5.7 , \mathrm { n } _ { 2 } = 38$

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?

As part of a marketing experiment, a department store regularly mailed discount coupons to 25 of its credit card holders. Their total credit card purchases over the next three months were compared to the credit card Purchases over the next three months for 25 credit card holders who were not sent discount coupons. Determine whether the samples are dependent or independent.

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 $\sigma { } _ { 1 } ^ { 2 } \neq \sigma _ { 2 } ^ { 2 }$ . Use $\alpha$ = 0.01. =18 =13 =520 =505 =40 =25

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. Test the claim that the salaries from both districts are equal. Assume the samples are random and independent, and the populations are normally distributed. Also, assume that $\sigma _ { 1 } ^ { 2 } = \sigma_ { 2 } ^{ 2 }$ Use $\alpha = 0.05 \text {. }$

Test the claim that $\mu _ { 1 } < \mu _ { 2 }$ Assume the two samples are random and independent. Use $\alpha = 0.05 .$ Population statistics: $\sigma _ { 1 } = 2.9 \text { and } \sigma _ { 2 } = 2.8$ Sample statistics: $\bar { x } 1 = 25.6 , n _ { 1 } = 35 \text { and } \bar { x } 2 = 28.15 , n _ { 2 } = 42$