Cullen (1994) took a sample of the 580 children served by an Auckland family practice to estimate the proportion of interest. What sample size in an SRS (without replacement) would he necessary to estimate the proportion with 95% confidence and margin of error 0.10? Cullen actually took an SRS with replacement of size 120, of whom 27 were not overdue for vaccination. Give a 95% CI for the proportion of children not overdue for vaccination

(1) The sample size required is 97.

(2) The 95% confidence interval for the proportion of children not overdue for vaccination is (0.15, 0.30).

Step-by-step explanation:

(1)

Let the proportion be, p = 0.50.

The margin of error formula is:

The critical value of z for 95% confidence level is,

z = 1.96 (Use the standard normal table for z values)

Compute sample size n as follows:

Thus, the sample size required is 97.

(2)

The confidence interval for population proportion is:

The sample size is, n = 120.

The number of children who were not overdue for vaccination, X = 27.

The sample proportion is:

The critical value of z for 95% confidence level is z = 1.96.

The 95% confidence interval is:

Thus, the 95% confidence interval for the proportion of children not overdue for vaccination is (0.15, 0.30).

proportions are fractions that equal to each other. so if two fractions are the same, they are proportional.

let's check the answers to see if they are proportional.

question a is not proportional because you can't turn 1.5/3 to 3/9. if you try to multiply 1.5/3 by 2 or 3, you wont get 3/9. it's impossible to make the fractions the same.

question b is not proportional because you can't turn 22/33 to 4/6. 33 can't go into 6.

question c is proportional because when you multiply 2 and 3 by 71, you would get 142/213, and those fractions equal to each other

question d is proportional because when you divide 14 and 7 by 2, you would end up with 7/3.5, and those fractions equal to each other.

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step-by-step explanation:

-6k+7k

(-6+7)k

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