Question

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 256 psi. A sample of 70 concrete cylinders was taken, and it was found that the average strength was 3000 psi. Find a 91% confidence interval for the true average strength of the concrete.

Be sure to:

• State the value for α.
• State whether you should use z or t and find the appropriate value. Round z-values to 2 decimals. Round t-values to 3 decimals.
• Find the confidence interval (to 2 decimals). State the parameter your confidence interval is for.
• Write a verbal interpretation of your confidence interval.

Answer 1

Explained below.

Explanation:

(1)

The confidence level is, 91%.

Compute the value of α as follows:

`\text{Confidence level}\% =(100-\alpha \%)\\\\91% = 100-\alpha \%\\\\\alpha \%=100-91\%\\\\\alpha \%=9\%\\\\\alpha =0.09`

(2)

As the population standard deviation is provided, i.e. σ = 256 psi, the z value would be appropriate.

The z value for α = 0.09 is,

z = 1.69

(3)

Compute the 91% confidence interval as follows:

`CI=\bar x\pm z_(\alpha/2)\cdot(\sigma)/(√(n))`

`=3000\pm 1.69\cdot(256)/(√(70))\\\\=3000\pm 51.71\\\\=(2942.29, 3057.71)`

(4)

The 91% confidence interval for population mean implies that there is a 0.91 probability that the true value of the mean is included in the interval, (2942.29, 3057.71) psi.