Question

In: Statistics and Probability

In a study of 4,000 individuals there are 1,632 individuals with diabetes. What is the proportion...

In a study of 4,000 individuals there are 1,632 individuals with diabetes. What is the proportion of individuals with diabetes and what is the 95% confidence interval for that proportion? Please Show all work done.

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Expert Solution

Solution:

Confidence Interval for population proportion(p)

Given,

n = 4000 ....... Sample size

x = 1632 .......no. of successes in the sample

Let denotes the sample proportion.

= x/n = 1632/4000 = 0.408

Our aim is to construct 95% confidence interval.

c = 0.95

= 1- c = 1- 0.95 = 0.05

/2 = 0.05 2 = 0.025 and 1- /2 = 0.975

Search the probability 0.975 in the Z table and see corresponding z value

= 1.96 for the 95% Confidence interval

Now , confidence interval for population proportion(p) is given by:

0.408 - 1.96* 0.408 + 1.96*

0.408 - 0.01523059993 < < 0.408 + 0.01523059993

0.3928 < < 0.4232

is the required 95% confidence interval for the population proportion.

Answer is (0.3928 , 0.4232)

orchestra answered 1 year ago

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