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Scorpion4ik [409]
2 years ago
11

An unconfined compression test was performed to determine the average strength of concrete cylinders (in psi). It is believed th

at 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.
Mathematics
1 answer:
Ronch [10]2 years ago
8 0

Answer:

Explained below.

Step-by-step 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. <em>σ</em> = 256 psi, the <em>z</em> value would be appropriate.

The <em>z</em> value for α = 0.09 is,

<em>z</em> = 1.69

(3)

Compute the 91% confidence interval as follows:

CI=\bar x\pm z_{\alpha/2}\cdot\frac{\sigma}{\sqrt{n}}

     =3000\pm 1.69\cdot\frac{256}{\sqrt{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.

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