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Chapter 7: Q. 9 (page 454)

Sample proportions List all 10possible SRSs of size n=2, calculate the proportion of females for each sample, and display the sampling distribution of the sample proportion on a dotplot.

Short Answer

Expert verified

The proportion of females :

Sample of size 2
Sample proportion of Female
Abigail - Bobby
0.5
Abigail - Carlos
0.5
Abigail - DeAnna
1
Abigail - Emily
1
Bobby - Carlos
0
Bobby - DeAnna
0.5
Bobby - Emily
0.5
Carlos - DeAnna
0.5
Carlos - Emily
0.5
DeAnna - Emily
1

The dotplot :

Step by step solution

01

Given information

We need to find proportion of females for each sample, and display the sampling distribution of the sample proportion 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

As given Size of sample is two.

Therefore, the proportion of females for each sample :

Sample of size 2
Sample proprtion of Female
Abigail - Bobby
p^=12=0.5
Abigail - Carlos
p^=12=0.5
Abigail - DeAnna
p^=22=1
Abigail - Emily
p^=22=1
Bobby - Carlos
p^=02=0
Bobby - DeAnna
p^=12=0.5
Bobby - Emily
p^=12=0.5
Carlos - DeAnna
p^=12=0.5
Carlos- Emily
p^=12=0.5
DeAnna - Emily
p^=22=1

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.

The dot plot is :

From dot plot

Centre =0.5

Minimum =0

Maximum =1

Range =1

Distribution is slightly negative of left skewed.

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Most popular questions from this chapter

Exercises 77 refer to the following setting. In the language of government statistics, you are "in the labor force" if you are available for work and either working or actively seeking work. The unemployment rate is the proportion of the labor force (not of the entire population) that is unemployed. Here are estimates from the Current Population Survey for the civilian population aged 25 years and over in a recent year. The table entries are counts in thousands of people.

Unemployment (1.1) Find the unemployment rate for people with each level of education. Is there an association between unemployment rate and education? Explain your answer.

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

Sample minimums List all 6possible SRSS of size n=2, calculate the minimum age for each sample, and display the sampling distribution of the sample minimum on a dotplot. Is the sample minimum an unbiased estimator of the population minimum? Explain your answer.

COLORAGE
RED1
WHITE5
SILVER8
RED20

More homework Some skeptical Ap庐 Statistics students want to investigate the newspaper's claim in Exercise 11, so they choose an SRS of 100students from the school to interview. In their sample, 45students completed their homework last week. Does this provide convincing evidence that less than 60%of all students at the school completed their assigned homework last week?

a. What is the evidence that less than 60%of all students completed their assigned homework last week?

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

We used technology to simulate choosing 250SRSs of size n=100n=100from a population of 2000students where 60%completed their assigned homework last week. The dotplot shows pp^the sample proportion of students who completed their assigned homework last week for each of the 250simulated samples.

c. There is one dot on the graph at 0.73. Explain what this value represents.

d. Would it be surprising to get a sample proportion of p=0.45p^=0.45or smaller in an SRS of size 100when p=0.60p=0.60? Justify your answer.

e. Based on your previous answers, is there convincing evidence that less than 60%of all students at the school completed their assigned homework last week? Explain your reasoning.

The student newspaper at a large university asks an SRS of 250 undergraduates, "Do you favor eliminating the carnival from the term-end celebration?" All in all, 150 of the 250 are in favor. Suppose that (unknown to you) 55\% of all undergraduates favor eliminating the carnival. If you took a very large number of SRSs of size n=250 n=250 from this population, the sampling distribution of the sample proportion p鈭�p^would be

a. exactly Normal with mean 0.55 and standard deviation 0.03.

b. approximately Normal with mean 0.55 and standard deviation 0.03.

c. exactly Normal with mean 0.60 and standard deviation 0.03.

d. approximately Normal with mean 0.60 and standard deviation 0.03.

e. heavily skewed with mean 0.55 and standard deviation 0.03.
See all solutions

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