Q 8.136. - Elementary Statistics

Question

Positively Selected Genes. R. Nielsen et al. compared $13.731$ 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 $14$ tissue types yielded the following number of genes. 

Step-by-Step Solution

Answer

It is not reasonable to apply the $t$-interval procedure to obtain the confidence interval of the population mean $\mu$ based on this sample.

Step 1: Given information

66	47	43	101	201	83	93
82	120	64	244	51	70	14

Step 2: Explanation

Now, draw a probability plot for the given data. 

Now construct a box plot for a given data. 

Step 3: Explanation

Now construct the histogram for the given data. 

 The sample size here is tiny $(n=14<15)$ The box plot and normal probability plot reveal that the sample contains two outliers. Also, because the plotted points do not lie roughly along a straight line, the normal probability plot indicates that the variable under discussion is not normally distributed. As a result, applying the $t-$interval approach to get the confidence interval of the population mean $\mu$ based on this sample is not reasonable.