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Chapter 7: Q.2 (page 458)

(a) Sketch a possible graph of the distribution of sample data for an SRS of size 5 with a range of 1000grams.

(b) Explain why the dotplot of sample ranges above is not the actual sampling distribution of the sample range.

Short Answer

Expert verified

(a)

(b)The range of both the distributions is not equal because the provided data plot has the range of 500samples while the actual one has the sample range for all the samples of 500size.

Step by step solution

01

Part(a) Step 1: Given information

Given in the question that, Researchers in Norway analyzed data on the birth weights of 400,000newborns over a six-year period. The distribution of birth weights is approximately Normal with a mean of 3668grams and a standard deviation of 511gra ms. I9n this population, the range (maximum 鈥� minimum) of birth weights is3417grams. We used Fathom software to take 500SRSs of size n=5and calculate the range (maximum 鈥� minimum) for each sample. The dotplot below shows the results.

  • We need to draw Sketch a possible graph of the distribution of sample data for an SRS of size 5with a range of 1000grams.
02

Part(a) Step 2: Explanation

Given,

Figure is,

Consider, the numbers are 2800,3000,3200,3400,3800.

The figure could be constructed as:

03

Part(b) Step 1: Given information

Researchers in Norway analyzed data on the birth weights of 400,000newborns over a six-year period. The distribution of birth weights is approximately Normal with a mean of 3668grams and a standard deviation of511grams.9In this population, the range (maximum 鈥� minimum) of birth weights is 3417grams. We used Fathom software to take 500SRSs of sizen=5and calculate the range (maximum 鈥� minimum) for each sample. The dotplot below shows the results

04

Part(b) Step 2: Explanation

The range of both the distributions is not equal because the provided data plot has the range of 500 samples while the actual one has the sample range for all the samples of 500 size.

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