A sample of 19 joint specimens of a particular type gave a sample mean proportional limit stress of 8.55 MPa and a sample standard deviation of 0.72 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.) 8.26 MPa

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A sample of 19 joint specimens of a particular type provided a sample mean proportional limit stress of 8.55 MPa and a sample standard deviation of 0.72 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.)**

Lower confidence bound: **8.26 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 greater than this value. ✔️

**What, if any, assumptions did you make about the distribution of proportional limit stress?**

- 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.)**

Lower prediction bound: **7.24 MPa** ❌
Transcribed Image Text:A sample of 19 joint specimens of a particular type provided a sample mean proportional limit stress of 8.55 MPa and a sample standard deviation of 0.72 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.)** Lower confidence bound: **8.26 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 greater than this value. ✔️ **What, if any, assumptions did you make about the distribution of proportional limit stress?** - 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.)** Lower prediction bound: **7.24 MPa** ❌
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