1. An unconfined compression test was performed to determine the average strength of concrete cylinders (in psi). It is believed that the strength is approximately normally distributed with a standard deviation of 225 psi. A sample of 60 concrete cylinders was taken, and it was found that the average strength was 2600 psi. Find a 93% confidence interval for the true average strength of the concrete.

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

[tex]\bar X=2600[/tex] represent the sample mean

[tex]\mu[/tex] population mean (variable of interest)

[tex]\sigma=225[/tex] represent the population standard deviation

n =60represent the sample size

Solution to the problem

The confidence interval for the mean is given by the following formula:

[tex]\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex] (1)

Since the Confidence is 0.93 or 93%, the value of [tex]\alpha=0.07[/tex] and [tex]\alpha/2 =0.035[/tex], and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.035,0,1)".And we see that [tex]z_{\alpha/2}=1.81[/tex]

Now we have everything in order to replace into formula (1):

[tex]2600-1.81\frac{225}{\sqrt{60}}=2547.424[/tex]

[tex]2600+1.81\frac{225}{\sqrt{60}}=2652.576[/tex]

So on this case the 93% confidence interval would be given by (2547.424;2652.576)