Question

#1)

A sample of 12 joint specimens of a particular type gave a sample mean proportional limit stress of 8.57 MPa and a sample standard deviation of 0.78 MPa.

(a) Calculate and interpret a 95% lower confidence bound for the true average proportional limit stress of all such joints. (Round your answer to two decimal places.)
_______ MPa

Interpret this bound. (pick one)

o With 95% confidence, we can say that the value of the true mean proportional limit stress of all such joints is centered around this value.

o With 95% confidence, we can say that the value of the true mean proportional limit stress of all such joints is less than this value.   

o With 95% confidence, we can say that the value of the true mean proportional limit stress of all such joints is greater than this value.

What, if any, assumptions did you make about the distribution of proportional limit stress? (pick one)

o We must assume that the sample observations were taken from a normally distributed population.

o We must assume that the sample observations were taken from a uniformly distributed population.    

o We do not need to make any assumptions.

o We must assume that the sample observations were taken from a chi-square distributed population.

(b) Calculate and interpret a 95% lower prediction bound for proportional limit stress of a single joint of this type. (Round your answer to two decimal places.)
_______ MPa

Interpret this bound. (pick one)

o If this bound is calculated for sample after sample, in the long run, 95% of these bounds will provide a lower bound for the corresponding future values of the proportional limit stress of a single joint of this type.

o If this bound is calculated for sample after sample, in the long run 95% of these bounds will provide a higher bound for the corresponding future values of the proportional limit stress of a single joint of this type.    

o If this bound is calculated for sample after sample, in the long run 95% of these bounds will be centered around this value for the corresponding future values of the proportional limit stress of a single joint of this type.

You may need to use the appropriate table in the Appendix of Tables to answer this question.

#2) An article reported that for a sample of 40 kitchens with gas cooking appliances monitored during a one-week period, the sample mean CO₂ level (ppm) was 654.16, and the sample standard deviation was 165.4.

(a) Calculate and interpret a 95% (two-sided) confidence interval for true average CO₂ level in the population of all homes from which the sample was selected. (Round your answers to two decimal places.)

( ____ , ____ ) ppm

Interpret the resulting interval. (pick one)

o We are 95% confident that this interval does not contain the true population mean.

o We are 95% confident that the true population mean lies below this interval.    

o We are 95% confident that this interval contains the true population mean.

o We are 95% confident that the true population mean lies above this interval.

(b) Suppose the investigators had made a rough guess of 170 for the value of s before collecting data. What sample size would be necessary to obtain an interval width of 56 ppm for a confidence level of 95%? (Round your answer up to the nearest whole number.)
______ kitchens

#3) It was reported that in a survey of 4713 American youngsters aged 6 to 19, 15% were seriously overweight (a body mass index of at least 30; this index is a measure of weight relative to height). Calculate a confidence interval using a 99% confidence level for the proportion of all American youngsters who are seriously overweight. (Round your answers to three decimal places.)

( _____ , _____ )

Please help with these questions. Thanks!

Answer 1

a) n=12 , d.f= n-1=12-1=11 mean= 8.57MPa and s= 0.78 Mpa , t(0.05, 11)= 1.80

95% confidence interval lower bound

A 95% lower confidence bound for the true average proportional limit stress of all such joints is:

8.57- 1.80* 0.78/sqrt(12)

8.57- 1.796*0.78/3.46

8.57-0.41= 8.16

With 95% confidence, the value of the true mean proportional limit stress of all such joints lies in the interval (8.16,infinity ). If this interval is calculated for sample after sample, in the long run 95% of these intervals will include the true mean proportional limit stress of all such joints. We must assume that the sample observations were taken from a normally distributed population.

b) 95% prediction interval is

8.57-1.796*(0.78)*sqrt(1+1/14)

8.57-1.401*1.035

8.57-1.45

7.12

If this bound is calculated for sample after sample, in the long run 95% of these bounds will provide a lower bound for the corresponding future values of the proportional limit stress of a single joint of this type.

NOTE:I have done the first question. Please repost the rest of the question. Thank you.