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Chapter 8: Q. R8.1 (page 547)

It’s 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 μ at a 99% confidence level based on an SRS of size 58

Short Answer

Expert verified

Part a) The critical value is1.88

Part b) The critical value is2.665

Step by step solution

01

Part a) Step 1: Given information

Confidence level=94%

Sample size (n)=125

02

Part a) Step 2: Calculation

Level of significance(α)=1-0.94=0.06

Using the standard normal, the critical value is set at6%

level of significance can be calculated as:

zα2=z0.062=1.88

Therefore, the critical value is1.88

03

Part b) Step 1: Given information

Confidence level=99%

Sample size (n)=58

04

Part b) Step 2: Calculation

Level of significance (α)=1-0.99=0.01

When the sample standard deviation is known, the t-critical value must be calculated.

The degree of freedom can be calculated as:

df=n-1=58-1=57

The critical value at the 1%level of significance is calculated as follows:

tα2,df=t0.012,57=2.665

Therefore, the critical value is2.665

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