# 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 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.]

### Probability and Statistics for Eng...

9th Edition
Jay L. Devore
Publisher: Cengage Learning
ISBN: 9781305251809

### Probability and Statistics for Eng...

9th Edition
Jay L. Devore
Publisher: Cengage Learning
ISBN: 9781305251809

#### Solutions

Chapter
Section
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 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.]

Expert Solution

a.

To determine

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

### Explanation of Solution

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.

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