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Chapter 8: Q 8.136. (page 344)

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.

Short Answer

Expert verified

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

Step by step solution

01

Given information

6647431012018393
8212064244517014
02

Explanation

Now, draw a probability plot for the given data.

Now construct a box plot for a given data.

03

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 μ based on this sample is not reasonable.

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Most popular questions from this chapter

Must the variable under consideration be normally distributed for you to use the z-interval procedure or t-interval procedure? Explain your answer.

M\&Ms. In the article "Sweetening Statistics-What M\&M's Can Teach Us" (Minitab Inc., August 2008), M. Paret and E. Martz discussed several statistical analyses that they performed on bags of M\&Ms. The authors took a random sample of 30 small bags of peanut M\&Ms and obtained the following weights, in grams (g).

a. Determine a 95%lower confidence bound for the mean weight of all small bags of peanut M\&Ms. (Note: The sample mean and sample standard deviation of the data are 52.040gand 2.807grespectively.)

b. Interpret your result in pant (a).

c. According to the package, each small bag of peanut M\&Ms should weigh 49.3gComment on this specification in view of your answer to part (b) It provides equal confidence with a greater lower limit.

Part (c) Because the weight of 49.3g is below the 95% lower confidence bound.

Assume that the population standard deviation is known and decide weather use of the z-interval procedure to obtain a confidence interval for the population mean is reasonable. Explain your answers.

The sample data contain no outliers, the variable under consideration is roughly normally distributed, and the sample size is 20.

A simple randoes sample is taken from a population and yields the following data for a variable of the population:

Find a point estimatate for the population mean.(i.e, the mean of the variable)

State True or False. Give Reasons for your answers.

The confidence level can be determined if you know only the margin of error, population standard deviation, and sample size.
See all solutions

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