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Math  /  Data & Statistics

QuestionQuestion 5 of 7
Determine the point estimate of the population mean and margin of error for the confidence interval. Lower bound is 16 , upper bound is 26 .
The point estimate of the population mean is □\square .
The margin of error for the confidence interval is □\square

Studdy Solution

STEP 1

What is this asking? We're given the lower and upper bounds of a confidence interval, and we need to find the **point estimate** of the population mean and the **margin of error**. Watch out! Don't mix up the point estimate and the margin of error!
The point estimate is the middle of the confidence interval, while the margin of error is the distance from the point estimate to either bound.

STEP 2

1. Calculate the Point Estimate
2. Calculate the Margin of Error

STEP 3

The **point estimate** is smack-dab in the middle of the confidence interval.
Think of it like the bullseye!
To find the middle, we **add** the **lower bound** and the **upper bound** and then **divide** by 2\text{2}.
It's like finding the average!

STEP 4

Point Estimate=Lower Bound+Upper Bound2 \text{Point Estimate} = \frac{\text{Lower Bound} + \text{Upper Bound}}{2}

STEP 5

Let's plug in our **lower bound** of 1616 and **upper bound** of 2626: Point Estimate=16+262 \text{Point Estimate} = \frac{16 + 26}{2}

STEP 6

Point Estimate=422 \text{Point Estimate} = \frac{42}{2}

STEP 7

Point Estimate=21 \text{Point Estimate} = 21 So, our **point estimate** is 2121!

STEP 8

The **margin of error** is the distance from the **point estimate** to either the **lower** or **upper bound**.
It's like measuring how far off our bullseye we are!
We can find this by **subtracting** the **lower bound** from the **point estimate** (or the **point estimate** from the **upper bound**).

STEP 9

Margin of Error=Point Estimate−Lower Bound \text{Margin of Error} = \text{Point Estimate} - \text{Lower Bound}

STEP 10

We just calculated our **point estimate** to be 2121, and our **lower bound** is 1616.
Let's plug those in: Margin of Error=21−16 \text{Margin of Error} = 21 - 16

STEP 11

Margin of Error=5 \text{Margin of Error} = 5 Awesome! Our **margin of error** is 55!

STEP 12

The point estimate of the population mean is 2121.
The margin of error for the confidence interval is 55.

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