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Chapter 7: Q. 10 (page 454)

Sample medians List all 10possible SRSs of size n=3, calculate the median quiz score for each sample, and display the sampling distribution of the sample median on a dotplot.

Short Answer

Expert verified

The median quiz score for each sample :

Sample size 3
Median
Abigail - Bobby - Carlos
(10,5,10)=10
Abigail - Bobby - DeAnna
(10,5,7)=7
Abigail - Bobby - Emily
(10,5,9)=9
Abigail - Carlos - DeAnna
(10,10,7)=10
Abigail - Carlos - Emily
(10,10,9)=10
Abigail - DeAnna - Emily
(10,7,9)=9
Bobby - Carlos - DeAnna
(5,10,7)=7
Bobby - Carlos - Emily
(5,10,9)=9
Carlos - DeAnna - Emily
(10,7,9)=9

The dot plot :

Step by step solution

01

Given information

We need to find the median quiz score for each sample, and display the sampling distribution of the sample median on a dotplot for given table

Name
Gender
Quiz score
Abigail
Female
10
Bobby
Male
5
Carlos
Male
10
DeAnna
Female
7
Emily
Female
9
02

Simplify

Median can be calculated by arranging the data in ascending or descending order.

The median quiz score for each sample :

Sample size
Median
Abigail - Bobby - Carlos
(10,5,10)=10
Abigail - Bobby - DeAnna
(10,5,7)=7
Abigail - Bobby - Emily
(10,5,9)=9
Abigail - Carlos - DeAnna
(10,10,7)=10
Abigail - Carlos - Emily
(10,10,9)=9
Abigail - DeAnna - Emily
(10,7,9)=9
Bobby - Carlos - DeAnna
(5,10,7)=7
Bobby - Carlos - Emily
(5,10,9)=9
Bobby - DeAnna - Emily
(5,7,9)=7
Carlos - DeAnna - Emily
(10,7,9)=9

A dot plot is a graph that shows the distribution of numerical variables by using dots to represent values.
If a value appears more than once in a whole number, the dots are stacked one on top of the other, with the height of the column of dots representing the frequency of that value.

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Most popular questions from this chapter

Finch beaks One dimension of bird beaks is "depth"-the height of the beak where it arises from the bird's head. During a research study on one island in the Galapagos archipelago, the beak depth of all Medium Ground Finches on the island was found to be Normally distributed with mean 渭=9.5鈥�millimeters(mm)and standard deviation 蟽=1.0mm.

a. Choose an SRS of 5 Medium Ground Finches from this population. Describe the sampling distribution of x炉.

b. Find the probability that x炉estimates 渭within 卤0.5mm. (This is the probability that x炉takes a value between 9 and 10 mm.

c. Choose an SRS of 50 Medium Ground Finches from this population. Now what is the probability that x炉falls within 卤0.05mmof 渭? In what sense is the larger sample "better"?

A sample of teens A study of the health of teenagers plans to measure the blood cholesterol levels of an SRS of 13to 16year-olds. The researchers will report the mean xfrom their sample as an estimate of the mean cholesterol level 渭in this population. Explain to someone who knows little about statistics what it means to say that xis an unbiased estimator of 渭.

The number of hours a lightbulb burns before failing varies from bulb to bulb. The population distribution of burnout times is strongly skewed to the right. The central limit theorem says that

a. as we look at more and more bulbs, their average burnout time gets ever closer to the mean 渭 for all bulbs of this type.

b. the average burnout time of a large number of bulbs has a sampling distribution with the same shape (strongly skewed) as the population distribution.

c. the average burnout time of a large number of bulbs has a sampling distribution with a similar shape but not as extreme (skewed, but not as strongly) as the population distribution.

d. the average burnout time of a large number of bulbs has a sampling distribution that is close to Normal.

e. the average burnout time of a large number of bulbs has a sampling distribution that is exactly Normal.

More sample minimums List all 4possible SRSs of size n=3, calculate the minimum age for each sample, and display the sampling distribution of the sample minimum on a dot plot with the same scale as the dot plot in Exercise 20. How does the variability of this sampling distribution compare with the variability of the sampling distribution from Exercise 20? What does this indicate about increasing the sample size?

From exercise20:

Car NumberColorAge
1
Red1
2
White5
3
Silver8
4
Red20

Bearings A production run of ball bearings is supposed to have a mean diameter of 2.5000centimeters (cm). An inspector chooses 100bearings at random from the run. These bearings have mean diameter 2.5009cm.

identify the population, the parameter, the sample, and the statistic.
See all solutions

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