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.
We are certain that the population mean is less than or equal to . i.e.
The formula used: One mean z- interval procedure
The lower confidence bound for the population mean is , which is
As a result, we are 100 percent certain that the population mean is larger than or equal to i.e.
level upper confidence bound for population means is
As a result, we are certain that the population mean is less than or equal to . i.e.
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.
Civilian Labor Force. Consider again the problem of estimating the mean age, , of all people in the civilian labor force. In Example on page 328 , we found that a sample size of 2250 is required to have a margin of error of year and a confidence level. Suppose that, due to financial constraints, the largest sample size possible is 900 . Determine the smallest margin of error, given that the confidence level is to be kept at . Recall that years.
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