Math

StatisticsProbability and Statistics for Engineering and the SciencesThe article “Distributions of Compressive Strength Obtained from Various Diameter Cores” ( ACI Materials J ., 2012: 597–606) described a study in which compressive strengths were determined for concrete specimens of various types, core diameters, and length-to-diameter ratios. For one particular type, diameter, and l/d ratio, the 18 tested specimens resulted in a sample mean compressive strength of 64.41 MPa and a sample standard deviation of 10.32 MPa. Normality of the compressive strength distribution was judged to be quite plausible. a. Calculate a confidence interval with confidence level 98% for the true average compressive strength under these circumstances. b. Calculate a 98% lower prediction bound for the compressive strength of a single future specimen tested under the given circumstances. [ Hint : t .02,17 = 2.224.]BuyFind*arrow_forward*

9th Edition

Jay L. Devore

Publisher: Cengage Learning

ISBN: 9781305251809

Chapter 7, Problem 48SE

Textbook Problem

The article **“Distributions of Compressive Strength Obtained from Various Diameter Cores” ( ACI Materials J., 2012: 597–606)** described a study in which compressive strengths were determined for concrete specimens of various types, core diameters, and length-to-diameter ratios. For one particular type, diameter, and

**a.**Calculate a confidence interval with confidence level 98% for the true average compressive strength under these circumstances.**b.**Calculate a 98% lower prediction bound for the compressive strength of a single future specimen tested under the given circumstances. [*Hint*:*t*_{.02,17}= 2.224.]

Expert Solution

**a.**

To determine

Find the 98% confidence interval for the population mean compressive strength of tested specimen.

**Given info:**

The sample mean compressive strength for a sample of 18 tested specimens is 64.41 MPa and the sample standard deviation of compressive strength is 10.32 MPa. Additionally it is mentioned that the population of tested specimens follows normal distribution.

**Calculation:**

*Confidence interval:*

**Software Procedure:**

Step by step procedure to obtain the 98% confidence interval to estimate the population mean compressive strength of tested specimen using the MINITAB software:

- Choose
**Stat > Basic Statistics > 1-Sample**.*t* - In
**Summarized data,**enter the sample size as**18**and sample mean as**64.41.** - Enter sample standard deviation as
**10.32.** - In
**Options**, enter**Confidence level**as**98...**

Expert Solution

**b.**

To determine

Find and interpret the 98% lower prediction bound for the compressive strength for a single future tested specimen.

Probability and Statistics for Engineering and the Sciences

Show all chapter solutions

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