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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

Sample proportions List all 6possible SRSS of size n=2, calculate the proportion of red cars in the sample, and display the sampling distribution of the sample proportion on a dotplot. Is the sample proportion an unbiased estimator of the population proportion? Explain your answer.

COLORAGE
RED1
WHITE5
SILVER8
RED20

10%Why is it important to check the 10 % condition before calculating probabilities involving localid="1654670795605">x-?

a. To reduce the variability of the sampling distribution of x-x¯

b. To ensure that the distribution of x-x¯is approximately Normal

c. To ensure that we can generalize the results to a larger population

d. To ensure that x-x¯will be an unbiased estimator of μ

e. To ensure that the observations in the sample are close to independent

Tall girls? To see if the claim made in Exercise 12is true at their high school, an Ap Statistics class chooses an SRS of twenty 16-year-old females at the school and measures their heights. In their sample, the mean height is 64.7inches. Does this provide convincing evidence that 16-year-old females at this school are taller than 64inches, on average?

a. What is the evidence that the average height of all 16-year-old females at this school is greater than 64inches, on average?

b. Provide two explanations for the evidence described in part (a).

We used technology to simulate choosing 250SRSs of size n=20from a population of three hundred 16-year-old females whose heights follow a Normal distribution with mean localid="1654113150676" μ=64inches and standard deviation μ=2.5inches. The dotplot shows x=the sample mean height for each of the 250simulated samples.

c. There is one dot on the graph at 62.5. Explain what this value represents.

d. Would it be surprising to get a sample mean of x=64.7or larger in an SRS of size 20when μ=64inches and σ=2.5inches? Justify your answer.

e. Based on your previous answers, is there convincing evidence that the average height of all 16-year-old females at this school is greater than 64inches? Explain your reasoning.

Making auto parts Refer to Exercise 54 . How many axles would you need to sample if you wanted the standard deviation of the sampling distribution of x-x¯to be 0.0005mm ? Justify your answer.

Bad eggs Selling eggs that are contaminated with salmonella can cause food poisoning in consumers. A large egg producer randomly selects 200 eggs from all the eggs shipped in one day. The laboratory reports that 9 of these eggs had salmonella contamination. Identify the population, the parameter, the sample, and the statistic.
See all solutions

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