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stich3 [128]
3 years ago
8

The compressive strength of concrete is being tested by a civil engineer who tests 12 specimens and finds that the sample mean i

s 3259.9 psi and the sample standard deviation is 35.57 psi. Compressive strength is known to be normally distributed.
Find a 95% confidence interval for mean compressive strength.
Mathematics
1 answer:
ki77a [65]3 years ago
6 0

Answer:

The 95% confidence interval for mean compressive strength is:

3237.3\leq \mu\leq 3282.5

Step-by-step explanation:

We have a sample of n=12 specimens, with sample mean=3259.9 and sample standard deviation = 35.57.

We know the population is normally distributed.

For a 95% confidence interval and df=n-1=11, the t-statistic is t=2.201.

Then, the CI can be expressed as:

M-t*s/\sqrt{N}\leq \mu\leq M+t*s/\sqrt{N}\\\\3259.9-2.201*35.57/\sqrt{12}\leq \mu\leq 3259.9+2.201*35.57/\sqrt{12}\\\\ 3259.9-22.6\leq \mu\leq 3259.9+22.6\\\\3237.3\leq \mu\leq 3282.5

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