Q.2 - The Practice of Statistics for AP

Question

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

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

Step-by-Step Solution

Answer

(a)

(b)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.

Part(a) Step 1: Given information

Given in the question that, Researchers in Norway analyzed data on the birth weights of $400,000$ newborns over a six-year period. The distribution of birth weights is approximately Normal with a mean of $3668$ grams and a standard deviation of $511$gra ms. I$9$n this population, the range (maximum – minimum) of birth weights is$3417$ grams. We used Fathom software to take $500$SRSs of size $n =5$and calculate the range (maximum – 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 $5$with a range of $1000$ grams.

Part(a) Step 2: Explanation

Given,

Figure is,

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

The figure could be constructed as:

Part(b) Step 1: Given information

Researchers in Norway analyzed data on the birth weights of $400,000$ newborns over a six-year period. The distribution of birth weights is approximately Normal with a mean of $3668$grams and a standard deviation of$511$ grams.$9$ In this population, the range (maximum – minimum) of birth weights is $3417$ grams. We used Fathom software to take $500$ SRSs of size$n =5$and calculate the range (maximum – minimum) for each sample. The dotplot below shows the results

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.