Chapter 8: Q 8.4RP. (page 346)
If you obtained one thousand confidence intervals for a population mean. , roughly how many of the intervals would actually contain ?
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A confidence interval for a population mean has a margin of error of
a. Determine the length of the confidence interval.
b. If the sample mean is , obtain the confidence interval.
c. Construct a graph that illustrates your results.
A simple random sample of size is taken from a population with an unknown standard deviation. A normal probability plot of the data displays significant curvature but no outliers. Can you reasonably apply the interval procedure? Explain your answer.
Positively Selected Genes. R. Nielsen et al. compared annotated genes from humans with their chimpanzee orthologs to identify genes that show evidence of positive selection. The researchers published their findings in "A Scan for Positively Selected Genes in the Genomes of Humans and Chimpanzees" (PLOS Biology, Vol. 3, Issue 6. Pp. 976-985). A simple random sample of tissue types yielded the following number of genes.
One-Sided One-Mean z-Intervals. Presuming that the assumptions for a one-mean z-interval are satisfied, we have the following formulas for -level confidence bounds for a population mean \(\mu\) :
- Lower confidence bound:
- Upper confidence bound:
Interpret the preceding formulas for lower and upper confidence bounds in words.
A confidence interval for a population mean has a length of .
a. Determine the margin of error.
b. If the sample mean is , determine the confidence interval.
c. Construct a graph that illustrates your results.
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