#1)

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

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

Interpret this bound. (pick one)

o With 95% confidence, we can say that the value of the truemean proportional limit stress of all such joints is centeredaround this value.

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

o With 95% confidence, we can say that the value of the truemean proportional limit stress of all such joints is greater thanthis value.

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

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

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

o We do not need to make any assumptions.

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

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

Interpret this bound. (pick one)

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

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

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

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

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

(a) Calculate and interpret a 95% (two-sided) confidenceinterval for true average CO₂ level in the population ofall homes from which the sample was selected. (Round your answersto two decimal places.)

( ____ , ____ ) ppm

Interpret the resulting interval. (pick one)

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

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

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

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

(b) Suppose the investigators had made a rough guess of 170 for thevalue of s before collecting data. What sample size wouldbe necessary to obtain an interval width of 56 ppm for a confidencelevel of 95%? (Round your answer up to the nearest wholenumber.)
______ kitchens

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

( _____ , _____ )

Please help with these questions. Thanks!