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Chapter 8: Q. 66 (page 519)

What critical value t⋆from Table B would you use for a 90%confidence interval for the population mean based on an SRS of size 77? If possible, use technology to find a more accurate value of t⋆. What advantage does the more accurate df provide?

Short Answer

Expert verified

The advantage of the more accurate degrees of freedom is that the confidence interval is going to be more accurate as well, thus the 90%confidence interval will be 90%confident of containing the true population mean of a SRS of size 77(while the less accurate degrees of freedom will result in the confidence interval being more than 90%confident of containing the true population mean as the critical value is larger).

Step by step solution

01

Given Information

Given

n=77

c=90%=0.90

The degrees of freedom is the sample size decreased by 1:

df=n-1=77-1=76

02

Explanation

Since table Bdoes not contain a row with df=76, use the row with a smaller degree of freedom that is closest to df=76:

df=60

The critical value t*can be found in table Bin the row with df=50and in the column with (1-c)/2=0.05:t*=1.671

When using technology (like for example, the Student's t-Distribution calculator on https://homepage.stat.uiowa.edu/~mbognar/applets/t.html) with df=77and 2P(X>x)=0.1, then you obtain x=1.665and thus a more accurate critical value is t*=1.665.

Table:t*=1.671Technology:t*=1.665

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