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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

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.

Bag check Thousands of travelers pass through the airport in Guadalajara, Mexico, each day. Before leaving the airport, each passenger must pass through the customs inspection area. Customs agents want to be sure that passengers do not bring illegal items into the country. But they do not have time to search every traveler's luggage. Instead, they require each person to press a button. Either a red or a green bulb lights up. If the red light flashes, the passenger will be searched by customs agents. A green light means "Go ahead." Customs agents claim that 30%of all travelers will be stopped (red light), because the light has probability of showing red on any push of the button. To test this claim, a concerned citizen watches a random sample of 100 travelers push the button. Only 20 get a red light.

a. Assume that the customs agents' claim is true. Find the probability that the proportion of travelers who get a red light in a random sample of 100 travelers is less than or equal to the result in this sample.

b. Based on your results in part (a), is there convincing evidence that less than 30%of all travelers will be stopped? Explain your reasoning.

A large company is interested in improving the efficiency of its customer service and decides to examine the length of the business phone calls made to clients by its sales staff. Here is a cumulative relative frequency graph from data collected over the past year. According to the graph, the shortest 80%of calls will take how long to complete?

a. Less than 10 minutes

b. At least 10 minutes

c. Exactly 10 minutes

d. At least 5.5minutes

e. Less than 5.5minutes

Which of the following statements about the sampling distribution of the sample mean is incorrect?

a. The standard deviation of the sampling distribution will decrease as the sample size increases.

b. The standard deviation of the sampling distribution measures how far the sample mean typically varies from the population mean.

c. The sample mean is an unbiased estimator of the population mean.

d. The sampling distribution shows how the sample mean is distributed around the population mean.

e. The sampling distribution shows how the sample is distributed around the sample mean.

A study of voting chose 663 registered voters at random shortly after an election. Of these, 72%said they had voted in the election. Election records show that only 56%of registered voters voted in the election. Which of the following statements is true?

a. 72%is a sample; 56%is a population.

b. 72%and 56%are both statistics.

c. 72%is a statistic and 56%is a parameter.

d. 72%is a parameter and 56%is a statistic.

e. 72%and 56%are both parameters.
See all solutions

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