Question

A random sample of 732 judges found that 405 were introverts. a. Construct a 95% confidence...

A random sample of 732 judges found that 405 were introverts.

a. Construct a 95% confidence interval for the proportion.

b. Interpret the meaning of the confidence interval. Justify your use of a confidence interval based on a normal distribution for data regarding proportions that are normally following a binomial distribution.

Note: Please show detailed working and justification.

Math   Statistics-And-Probability   
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Answer #1

Here it is given that n=735 and x=405

So

a. Now for 95% CI z value is 1.96

Hence Margin of Error is

Sp CI is

b. As per the confidence interval population proportion will lie in the range of (0.532,0.568)

Now as it says that distribution is binomial, so we find that np>10 and npq>10. Also n is sufficient large so we consider the normal approximation for binomial distribution.

Based on this we have used z value to find the confidence interval in part a.

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