Question

Five books An author has written 5 children's books. The numbers of pages in these books are $64,66,71,73$, and 76 .

a. List all 10 possible SRSs of size $\mathrm{n}=3,n=3$, calculate the median number of pages for each sample, and display the sampling distribution of the sample median on a dotplot.

b. Describe how the variability of the sampling distribution of the sample median would change if the sample size was increased to $\mathrm{n}=4.n=4$.

c. Construct the sampling distribution of the sample median for samples of size $n=4$. $n=4$. Does this sampling distribution support your answer to part (b)? Explain your reasoning.

Short answer

(a)

In the above dot plot graph the associating number on the line which is looking forth

(b)The estimates are more accurate, then the estimates will vary less from the true population value and therefore the variability of the sampling distribution decreases.

(c)It is observed that the medians of the sample in the sampling distribution for $\mathrm{n}=4$then indeed vary less than the sample medians in the sampling distribution for $n=3$, which supports the answer in part (b)

Step-by-step solution

Part (a) Step 1: Given Information

The numbers of pages in these books are $64,66,71,73,76$

Part (a) Step 2: Simplification

Three of the five population values are represented in a sample of size $n=3.$

The sample median is the middle value of the sample's data values.

In the above dot plot graph the associating number on the line which is looking forth,

Part (b) Step 1: Given Information

The numbers of pages in these books are $64,66,71,73,76$

Part (b) Step 2: Simplification

Here, we want to increase the sample size from $n=3\circ n=4$

By expanding the sample size, more information about the population is obtained, and hence the estimations are more accurate.

If the estimates are more precise, they will deviate less from the true population value, reducing the variability of the sampling distribution.

Part (c) Step 1: Given Information

The numbers of pages in these books are $64,66,71,73,76$

Part (c) Step 2: Simplification

Consider,

The sample median

For $\mathrm{n}=3$, The sampling distribution's median ranges from 66 to 73, and for $n=4$, The sampling distribution's sample medians vary from 68.5 to 72. .

It is discovered that the sample medians in the sampling distribution for $n=4$therefore the sample medians in the sampling distribution do indeed vary less than the sample medians for$n=3$, which supports the answer in part (b)