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Chapter 8: Q. T8.5 (page 549)

You want to compute a 90%confidence interval for the mean of a population with an unknown population standard deviation. The sample size is 30. What critical value should you use for this interval?

a. 1.645

b. 1.699

c. 1.697

d. 1.96

e. 2.045

Short Answer

Expert verified

The critical value that should be used in this interval is1.699

The required correct option is (b)

Step by step solution

01

Given information

The standard deviation of the population is unknown.

Sample size (n)=30

Confidence level =90%

02

The objective is to find out the critical value that should be used in this interval

The level of significance is:

Level of significance (伪)=1-Confidence level

=1-0.90=0.10

The t-critical value must be calculated here.

The degree of freedom is calculated as follows:

localid="1654412235779" (df)=n-1=30-1=29

The critical value at 29degrees of freedom and a 10%significance level is calculated as follows:

t伪2,df=t0.102,29=1.699

Therefore, the correct option is(b)

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