Chapter 8: Q 32 (page 478)

Identify the following specifications:
a. lower limit
b. upper limit
c. error bound

Short Answer

Expert verified

The lower limit is 24.52 $t h e 95 \ % c o n f i d e n c e i n t e r v a l i s 24.52$

The upper limit is 36.28

The error bound is 5.88

Step by step solution

Given Information (a)

The sample mean is $30.4$ , that is, $\bar{x} = 30.4$

The confidence level is

95 %

, that is,

α = 0.05

We have to find lower limit

Explanation of (b)

The lower limit is calculated using the formula given below,

Lower Limit $= \bar{x} - z_{\frac{a}{2}} \frac{σ}{\sqrt{n}}$

The calculation is given below,

Lower Limit $= \bar{x} - z_{0.025} \frac{σ}{\sqrt{n}}$

$= 30.4 - 1.96 \times \frac{15}{\sqrt{25}}$

$= 30.4 - 1.96 \times 3$

=24.52

Given Information of (b)

The sample mean is $30.4$ , that is, $\bar{x} = 30.4$ .

The confidence level is $95 %$ , that is, $α = 0.05$

We have to find upper bound

Calculation of upper bound

The upper limit calculation formula is given below

Upper bound= $\bar{x} + z_{\frac{a}{2}} \frac{σ}{\sqrt{n}}$ $= \bar{x} + z_{\frac{a}{2}} \frac{σ}{\sqrt{n}}$

$= 30.4 + 1.96 \times \frac{15}{\sqrt{25}}$

$= 30.4 + 1.96 x 3$

=36.28

Given Information of (c)

The sample mean is $30.4$ , that is, $\bar{x} = 30.4$ .

The confidence level is $95 %$ , that is, $α = 0.05$

We have to find the error bound

Calculation of Error Bound

The error bound is calculated using the formula given below,

$E B M = z_{\frac{a}{2}} \frac{σ}{\sqrt{n}}$

$E B M = z_{0.025} \frac{15}{\sqrt{25}}$

$= 1.96 \times \frac{15}{5}$

=5.88

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Identify the following specifications:
a. lower limit
b. upper limit
c. error bound

Short Answer

Step by step solution

Given Information (a)

Explanation of (b)

Given Information of (b)

Calculation of upper bound

Given Information of (c)

Calculation of Error Bound

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Identify the following specifications:a. lower limitb. upper limitc. error bound

Short Answer

Step by step solution

Given Information (a)

Explanation of (b)

Given Information of (b)

Calculation of upper bound

Given Information of (c)

Calculation of Error Bound

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Calculus

Logic and Functions

Mechanics Maths

Statistics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Identify the following specifications:
a. lower limit
b. upper limit
c. error bound