Use the given data to find the minimum sample size required to estimate the population proportion. a. Margin of error: 0.004: confidence level: 95% p and q unknown
b. Margin of error: 0.009, confidence level: 99%; p and q unknown
c. Margin of error: 0.01; confidence level: 95%; from a prior study, p is estimated by the decimal equivalent of 52%.

a. The minimum sample size required is of 60,025.

b. The minimum sample size required is of 20,465.

c. The minimum sample size required is 9,589.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of , and a confidence level of , we have the following confidence interval of proportions.

In which

z is the z-score that has a p-value of .

The margin of error is of:

Question a:

95% confidence level

So , z is the value of Z that has a p-value of , so .

p and q unknown means that we use , which is when the largest sample size is needed.

Margin of error: 0.004

We have to find n for which M = 0.004. So

The minimum sample size required is of 60,025.

b. Margin of error: 0.009, confidence level: 99%; p and q unknown

99% confidence level

So , z is the value of Z that has a p-value of , so .

Margin of error: 0.009

We have to find n for which M = 0.009. So

Rounding up:

The minimum sample size required is of 20,465.

c. Margin of error: 0.01; confidence level: 95%; from a prior study, p is estimated by the decimal equivalent of 52%.

Here we have .

The minimum sample size is n for which M = 0.01. So

Rounding up:

The minimum sample size required is 9,589.

hello :

by applying the distributive property :

6 × 4.3 = 6 × ( 4 + 0.3 )

            =   (6 ×   4) + (6 ×   0.3)

            = 24 + 1.8

6 × 4.3 = 25.8

c. 27 units.

step-by-step explanation:

we are told that in circle a, ∠bae ≅ ∠dae.

we can see from our given diagram that in and ;

, as these are radii of our given circle.

therefore, by sas congruence postulate.

hence, side be will be equal to side de as corresponding parts of congruent triangles are congruent. so we can set an equation to find the value of x as:

now let us substitute x=17 in the expression for the length of be.

therefore, length of be will be 27 units and option c is the correct choice.