# Large sample test for population mean

1. May 6, 2017

### Poke

1. The problem statement, all variables and given/known data

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 μ 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 test is made of H0:μ ≤1350 versus H1:μ>1350.

a. Find the P-value.
b. Do you believe it is plausible that the blocks do not meet the speciﬁcation, or are you convinced that they do? Explain your reasoning.

2. Relevant equations
It is asking for Population Mean, with large sample (n=100)
H0:μ ≤1350 ; H1:μ>1350 ; μ0 = 1350

Z = \frac{Mean - μ0}{ \frac{\sigma}{\sqrt{n}} }

3. The attempt at a solution
As H1:μ> μ0 , Area to the right of Z

Z = 0.8571, between 0.8023 and 0.8051
so P = 1 - \frac{0.8023+0.8051}{2}
P = 0.1963 > 0.05 (5%) = \alpha

So we cannot reject H0, and we can only conclude the blocks do not meet the speciﬁcation is plausible.

Am I doing it in a correct approach, and final answer correct? Thanks!

2. May 6, 2017

### Staff: Mentor

It is possible, yes, you cannot exclude it.