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Nookie1986 [14]
2 years ago
9

Construct a confidence interval of the population proportion at the given level of confidence.

Mathematics
1 answer:
scZoUnD [109]2 years ago
7 0

Answer:

The lower bound of the confidence interval is 0.6922.

Step-by-step explanation:

We have to calculate a 94% confidence interval for the proportion.

The sample proportion is p=0.7167.

p=X/n=860/1200=0.7167

The standard error of the proportion is:

\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.7167*0.2833}{1200}}\\\\\\ \sigma_p=\sqrt{0.000169}=0.013

The critical z-value for a 94% confidence interval is z=1.8808.

The margin of error (MOE) can be calculated as:

MOE=z\cdot \sigma_p=1.8808 \cdot 0.013=0.0245

Then, the lower and upper bounds of the confidence interval are:

LL=p-z \cdot \sigma_p = 0.7167-0.0245=0.6922\\\\UL=p+z \cdot \sigma_p = 0.7167+0.0245=0.7412

The 94% confidence interval for the population proportion is (0.6922, 0.7412).

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