1. Let x_1,x_2,… ,x_n be an independent sample from a normal distribution 1). For the following test problem: , let the rejection region be W={(x_1,x_2,… ,x_n ): √n ¯x_n<-1.65}.

a. What is the α of this test?

b. When μ≤-0.1, in order to make sure that β≤0.05, how large n you need?

2. The objective of a randomized controlled trial by Adab et al. (A-19)was to determine whether providing

women with additional information on the pros and cons of screening for cervical cancer would increase

the willingness to be screened. A treatment group of 138 women received a leaflet on screening that

contained more information (average individual risk for cervical cancer, likelihood of positive finding,

the possibility of false positive/negative results, etc.) than the standard leaflet developed by the British

National Health Service that 136women in a control group received. In the treatment group, 109women

indicated they wanted to have the screening test for cervical cancer while in the control group, 120

indicated they wanted the screening test. Construct a 95 percent confidence interval for the difference in

proportions for the two populations represented by these samples.

3. Ho et al. (A-25) used telephone interviews of randomly selected respondents in Hong Kong to obtaining formation regarding individuals’ perceptions of health and smoking history. Among 1222 current male smokers, 72 reported that they had “poor” or “very poor” health, while 30 among 282 former male smokers reported that they had “poor” or “very poor” health. Is this sufficient evidence to allow one to conclude that among Hong Kong men there is a difference between current and former smokers with respect to the proportion who perceive themselves as having “poor” and “very poor” health? Let ï„ƒ= 0.01

4. There are seven types of artificial man-made fibers, 4 pieces were taken from each type to test their strengths. The summery of the date is given as the following:

5. Types 1 Type 2 Type 3 Type 4 Type 5 Type 6 Type 7

6.

7.

a. you don’t know the raw data but the summary of it, is it enough to find a 95% confidence interval for the common σ? If so, find it

5. Let

1. Let x_1,x_2,… ,x_n be an independent sample from a normal distribution 1). For the following test problem: , let the rejection region be W={(x_1,x_2,… ,x_n ): √n ¯x_n<-1.65}.

a. What is the α of this test?

b. When μ≤-0.1, in order to make sure that β≤0.05, how large n you need?

2. The objective of a randomized controlled trial by Adab et al. (A-19)was to determine whether providing

women with additional information on the pros and cons of screening for cervical cancer would increase

the willingness to be screened. A treatment group of 138 women received a leaflet on screening that

contained more information (average individual risk for cervical cancer, likelihood of positive finding,

the possibility of false positive/negative results, etc.) than the standard leaflet developed by the British

National Health Service that 136women in a control group received. In the treatment group, 109women

indicated they wanted to have the screening test for cervical cancer while in the control group, 120

indicated they wanted the screening test. Construct a 95 percent confidence interval for the difference in

proportions for the two populations represented by these samples.

3. Ho et al. (A-25) used telephone interviews of randomly selected respondents in Hong Kong to obtaining formation regarding individuals’ perceptions of health and smoking history. Among 1222 current male smokers, 72 reported that they had “poor” or “very poor” health, while 30 among 282 former male smokers reported that they had “poor” or “very poor” health. Is this sufficient evidence to allow one to conclude that among Hong Kong men there is a difference between current and former smokers with respect to the proportion who perceive themselves as having “poor” and “very poor” health? Let ï„ƒ= 0.01

4. There are seven types of artificial man-made fibers, 4 pieces were taken from each type to test their strengths. The summery of the date is given as the following:

5. Types 1 Type 2 Type 3 Type 4 Type 5 Type 6 Type 7

6.

7.

a. you don’t know the raw data but the summary of it, is it enough to find a 95% confidence interval for the common σ? If so, find it

5. Let

1. Let x_1,x_2,… ,x_n be an independent sample from a normal distribution 1). For the following test problem: , let the rejection region be W={(x_1,x_2,… ,x_n ): √n ¯x_n<-1.65}.

a. What is the α of this test?

b. When μ≤-0.1, in order to make sure that β≤0.05, how large n you need?

2. The objective of a randomized controlled trial by Adab et al. (A-19)was to determine whether providing

women with additional information on the pros and cons of screening for cervical cancer would increase

the willingness to be screened. A treatment group of 138 women received a leaflet on screening that

contained more information (average individual risk for cervical cancer, likelihood of positive finding,

the possibility of false positive/negative results, etc.) than the standard leaflet developed by the British

National Health Service that 136women in a control group received. In the treatment group, 109women

indicated they wanted to have the screening test for cervical cancer while in the control group, 120

indicated they wanted the screening test. Construct a 95 percent confidence interval for the difference in

proportions for the two populations represented by these samples.

3. Ho et al. (A-25) used telephone interviews of randomly selected respondents in Hong Kong to obtaining formation regarding individuals’ perceptions of health and smoking history. Among 1222 current male smokers, 72 reported that they had “poor” or “very poor” health, while 30 among 282 former male smokers reported that they had “poor” or “very poor” health. Is this sufficient evidence to allow one to conclude that among Hong Kong men there is a difference between current and former smokers with respect to the proportion who perceive themselves as having “poor” and “very poor” health? Let ï„ƒ= 0.01

4. There are seven types of artificial man-made fibers, 4 pieces were taken from each type to test their strengths. The summery of the date is given as the following:

5. Types 1 Type 2 Type 3 Type 4 Type 5 Type 6 Type 7

6.

7.

a. you don’t know the raw data but the summary of it, is it enough to find a 95% confidence interval for the common σ? If so, find it

5. Let

Subject | Mathematics |

Due By (Pacific Time) | 12/03/2014 10:00 am |

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