Question

Suppose a 95% confidence interval for a population proportion is (0.30, 0.60). Rewrite this interval in the form of margin of error.​

Answer 1

Answer:

This interval in the form of margin of error is expressed as 0.45 ± 0.15.

p = 0.45

MOE = 0.15

Step-by-step explanation:

A confidence interval is calculated from a sample statistic (in this case, a sample proportion) and substracted or added a margin of error (MOE) for the lower and upper bound respectively.

This can be expressed as:

$LL=p-MOE\\\\UL=p+MOE$

If we substract the upper bound from the lower bound, we can calculate the margin of error as:

$UL-LL=(p+MOE)-(p-MOE)=2\cdot MOE\\\\MOE=\dfrac{UL-LL}{2}=\dfrac{0.60-0.30}{2}=0.15$

With this information, we can calculate the sample proportion p:

$LL=p-MOE=p-0.15=0.30\\\\p=0.30+0.15=0.45$

Then, we can express the confidence interval as:

$p\;\pm\;MOE=0.45\pm0.15$

Answer 2

The interval in the form of margin of error is expressed as 0.45±0.15

To get the margin of error for the 95% confidence interval for a population proportion, we will use the formula;

$MOE =\frac{Ub-Lb}{2} \\MOE =\frac{0.60-0.30}{2}\\MOE =\frac{0.30}{2} \\MOE =0.15$

Get the interval form of margin of error. The margin of error is expressed as:

$Interval = P\pm0.15\\interval = (0.30+0.15)\pm 0.15\\interval = 0.45\pm 0.15$

Hence the interval in the form of margin of error is expressed as 0.45±0.15

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