Question

A sample of 17 joint specimens of a particular type gave a sample mean proportional limit stress f 8.44 MPa and a sample standard deviation of 0.75 MPa. two decimal places.) (a) Calculate and interpret a 95% lower confidence bound for the true average proportional limit stress of all such joints. (Round your answer MPa Interpret this bound. 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. 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. 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? We do not need to make any assumptions. We must assume that the sample observations were taken from a chi-square distributed population. We must assume that the sample observations were taken from a uniformly distributed population. We must assume that the sample observations were taken from a normally 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. f the proportional OIf 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 limit stress of a single joint of this type. 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 a single joint of this type. proportional limit stress 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

Answer 1

Solution:

Sample size, n = 17

Sample mean, mPa

T = 8,44

Sample Standard Deviation, s = 0.75 mPa.

The critical value for 95% confidence interval is, t = 1.746

The 95% confidence interval is,

t +t* - n 8.1224, 8.7576)

The lower bound is = 8.1224 MPa. = 8.12 MPa

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

We do not need to make any assumptions.

95% prediction bound is given by:

t ] 17.17,9.71] /1 t 1 /1 +

The lower 95% prediction bound = 7.17 MPa.

The correct interpretation is (c) lower bound.