A new concrete mix is being designed to provide adequate compressive strength fo

Question

A new concrete mix is being designed to provide adequate compressive strength for concrete blocks.  The specification for a particular application calls for the blocks to have a mean compressive strength greater than 1350 kPa.  A sample of 100 blocks is produced and tested.  Their mean compressive strength is 1356 kPa and their standard deviation is 70 kPa. 

a) Is it Plausible that the blocks do not meet specifications, or do they? Explain a reasoning by carrying out the appropriate hypothesis test.

b)If a sample of 10 blocks is produced and tested with their mean compressive strength at 1372 kPa and their standard deviation at 68 kPa.  Find the P-value based on the same hypothesis.

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Explanation / Answer

Given n=100, xbar= 1356, s=70

(1) The test hypothesis is
Ho:<=1350
Ha:>1350

The test statistic is

Z=(xbar-)/(s/n)

=(1356-1350)/(70/10)

= 0.86

If a=0.05, the critical value is Z(0.05)=1.645 (check standard normal table)

Since Z=0.86<1.645, we do not reject Ho.

So we can conclude the blocks do not meet specifications.

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(2)Given n=10, xbar =1372, s=68

Z=(1372-1350)/(68/sqrt(10)) = 1.02

The p-vlaue is P(Z> 1.02)= 0.1539 (check standard normal table)

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