Chapter 7, Problem R7.2RE

(a)

To determine

To Calculate: the median number of pages for each sample, and display the sampling distribution of the sample median on a dot plot.

Answer to Problem R7.2RE

Sample of size 3	Median
64, 66, 71	66
64, 66, 73	66
64, 66, 76	66
64, 71, 73	71
64, 71, 76	71
64, 73, 76	73
66, 71, 73	71
66, 71, 76	71
66, 73, 76	73
71, 73, 76	73

Explanation of Solution

Given:

64, 66, 71, 73, 76

Calculation:

A sample of size n=3 contains 3 of the 5 population values

Sample of size 3
64, 66, 71
64, 66, 73
64, 66, 76
64, 71, 73
64, 71, 76
64, 73, 76
66, 71, 73
66, 71, 76
66, 73, 76
71, 73, 76

Sample median would be the middle value of the data values in the sample

Sample of size 3	Median
64, 66, 71	66
64, 66, 73	66
64, 66, 76	66
64, 71, 73	71
64, 71, 76	71
64, 73, 76	73
66, 71, 73	71
66, 71, 76	71
66, 73, 76	73
71, 73, 76	73

Graph:

  

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

(b)

To determine

To Explain: the variability of the sampling distribution of the sample median would change if the sample size was increased to n=4.

Answer to Problem R7.2RE

Variability decreases

Explanation of Solution

Here are interested in increasing the sample size from n= 3 o n=4

It the increasing the sample size, then it will give more information about the population and therefore the estimates are more accurate.

If 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)

To determine

To construct: the sampling distribution of the sample median for samples of size n=4 and this sampling distribution support the answer to part (b).

Answer to Problem R7.2RE

Yes

Explanation of Solution

Given:

Population values: 64, 66, 71, 73, 76

Calculation:

Sample of size 4

64, 66, 71, 73

64, 66, 71,76

64, 66, 73, 76

64, 71, 73, 76

66, 71, 73, 76

Sample median

Sample of size 4	Median
64, 66, 71, 73	$\frac{66+71}{2}=68.5$
64, 66, 71,76	$\frac{66+71}{2}=68.5$
64, 66, 73, 76	$\frac{66+73}{2}=69.5$
64, 71, 73, 76	$\frac{71+73}{2}=72$
66, 71, 73, 76	$\frac{71+73}{2}=72$

Graph:

  

For n=3, the median of sample in the sampling distribution range from 66 to 73 and for n=4, the sample medians in the sampling distribution range from 68.5 to 72.

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