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Chapter 8: Q.2 (page 522)

It鈥檚 critical Find the appropriate critical value for constructing a confidence interval in each of the following settings.

(a) Estimating a population proportion p at a 94%confidence level based on an SRS of size 125.

(b) Estimating a population mean M at a 99%confidence level based on an SRS of size 58.

Short Answer

Expert verified

a). The critical value is 1.96.

b). The critical value is 2.576.

Step by step solution

01

Part (a) Step 1: Given Information

Population proportion (p)=94%=0.94.

Sample size (n)=125.

02

Part (a) Step 2: Explanation

The level of significance is:

Level of significance =1-Confidence level

=1-0.95

=0.05

The critical value using standard normal table is calculated as:

z伪/2=z0.05/2

=z0.025

=1.96

The critical value is 1.96.

03

Part (b) Step 1: Given Information

Confidence level =99%.

Sample size (n)=58.

04

Part (b) Step 2: Explanation

The level of significance is:

Level of significance =1-Confidence level

=1-0.99

=0.01

The critical value using the standard normal table is calculated as:

za/2=z0.01/2

=z0.005

=2.576

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