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Lesson Example Discussion Quiz: Class Homework

Quiz At Home

Title: Evaluating and Inference Sample Statistics

Grade: 1400-a Lesson: S4-L4

Explanation: Hello Students, time to practice and review. Let us take next 10-15 minutes to solve the ten problems using the Quiz Sheet. Then submit the quiz to get the score. This is a good exercise to check your understanding of the concepts.

Quiz: at Home

Problem Id	Problem	Options
1	The members of a city council wanted to assess the opinions of all city residents about converting an open field into a dog park. The council surveyed a sample of 500 city residents who own dogs. The survey showed that the majority of those sampled were in favor of the dog park. Which of the following is true about the city council’s survey?	A) The survey sample should have included more residents who are dog owners. B) The survey sample should have consisted entirely of residents who do not own dogs. C) The survey sample is biased because it is not representative of all city residents. D) It shows that the majority of city residents are in favor of the dog park.
2	A certain forest is 253 acres. To estimate the number of trees in the forest, a ranger randomly selects 5 different 1-acre parcels in the forest and determines the number of trees in each parcel. The numbers of trees in the sample acres are 51, 59, 45, 52, and 73. Based on the mean of the sample, which of the following ranges contains the best estimate for the number of trees in the entire forest?	A) 11,000 to 12,000 B) 12,500 to 13,500 C) 18,000 to 19,000 D) 13,500 to 14,500
3	Residents of a town were surveyed to determine whether they are satisfied with the concession stand at the local park. A random sample of 200 residents was selected. All 200 responded, and 87% said they are satisfied. Based on this information, which of the following statements must be true? I. Of all the town residents, 87% would say they are satisfied with the concession stand at the local park. II. If another random sample of 200 residents were surveyed, 87% would say they are satisfied.	A) I only B) Neither C) II only D) I and II
4	A survey was conducted using a sample of history professors selected at random from the California State Universities. The professors surveyed were asked to name the publishers of their current texts. What is the largest population to which the results of the survey can be generalized?	A) All history professors at all California State Universities. B) All professors in the United States. C) All history professors in the United States. D) All professors at all California State Universities.
5	In a study investigating the average time spent commuting to work for residents in a city, a random sample of 100 residents was taken. The sample mean commuting time was found to be 25 minutes, with a standard deviation of 5 minutes. 1. What is the 95% confidence interval for the average time spent commuting to work for all residents in the city? 2. If the researchers want to decrease the margin of error in their estimate while keeping the confidence level at 95%, what should they do?	A) 25 ± 0.98 B) 24 ± 0.94 C) 25 ± 0.89 D) 23 ± 0.98
6	A trivia tournament organizer wanted to study the relationship between the number of points a team scores in a trivia round and the number of hours that a team practices each week. For the study, the organizer selected teams at random from all trivia teams in a certain tournament. The table displays the information for the teams in the sample that practiced for at least hours per week. Which of the following is the largest population to which the results of the study can be generalized? $6$	A) The 40 trivia teams in the sample that practiced for at least 3 hours per week. B) All trivia teams in the tournament. C) The 55 trivia teams in the sample. D) All trivia teams in the tournament that scored 14 or more points in the round.
7	A random sample of 400 town voters were asked if they plan to vote for Candidate A or Candidate B for mayor. The results were sorted by gender and are shown in the table below. The town has a total of 6,000 voters. Based on the table, what is the best estimate of the number of voters who plan to vote for Candidate A? $7$	A) 3,550 B) 3,540 C) 3,450 D) 3,570
8	In a survey conducted in a city with a population of 50,000, a random sample of 500 residents was asked about their preferred mode of transportation to work. Among the sample, 200 residents reported using cars as their primary mode of transportation. What is the estimated number of residents in the city who use cars as their primary mode of transportation to work?	A) 20,100 B) 19,900 C) 20,000 D) 19,800
9	In a city with a population of 10,000 residents, a survey is conducted to determine the proportion of residents who support a new public transportation initiative. A random sample of 500 residents is taken, and it is found that 250 of them support the initiative. Based on this sample, estimate the total number of residents in the city who support the new public transportation initiative.	A) 5100 B) 4900 C) 5000 D) 4750
10	In a survey conducted among 150 members of a fitness club, 60 members indicated that they are interested in participating in a new yoga class. The fitness club has a total membership of 500 members. Based on this survey, estimate how many members in total would be interested in participating in the new yoga class.	A) 190 B) 210 C) 195 D) 200

Problem Id

Problem

Options

The members of a city council wanted to assess the opinions of all city residents about converting an open field into a dog park. The council surveyed a sample of 500 city residents who own dogs. The survey showed that the majority of those sampled were in favor of the dog park. Which of the following is true about the city council’s survey?

A) The survey sample should have included more residents who are dog owners.

B) The survey sample should have consisted entirely of residents who do not own dogs.

C) The survey sample is biased because it is not representative of all city residents.

D) It shows that the majority of city residents are in favor of the dog park.

A certain forest is 253 acres. To estimate the number of trees in the forest, a ranger randomly selects 5 different 1-acre parcels in the forest and determines the number of trees in each parcel. The numbers of trees in the sample acres are 51, 59, 45, 52, and 73. Based on the mean of the sample, which of the following ranges contains the best estimate for the number of trees in the entire forest?

A) 11,000 to 12,000

B) 12,500 to 13,500

C) 18,000 to 19,000

D) 13,500 to 14,500

Residents of a town were surveyed to determine whether they are satisfied with the concession stand at the local park. A random sample of 200 residents was selected. All 200 responded, and 87% said they are satisfied. Based on this information, which of the following statements must be true?
I. Of all the town residents, 87% would say they are satisfied with the concession stand at the local park.
II. If another random sample of 200 residents were surveyed, 87% would say they are satisfied.

A) I only

B) Neither

C) II only

D) I and II

A survey was conducted using a sample of history professors selected at random from the California State Universities. The professors surveyed were asked to name the publishers of their current texts. What is the largest population to which the results of the survey can be generalized?

A) All history professors at all California State Universities.

B) All professors in the United States.

C) All history professors in the United States.

D) All professors at all California State Universities.

In a study investigating the average time spent commuting to work for residents in a city, a random sample of 100 residents was taken. The sample mean commuting time was found to be 25 minutes, with a standard deviation of 5 minutes.

1. What is the 95% confidence interval for the average time spent commuting to work for all residents in the city?
2. If the researchers want to decrease the margin of error in their estimate while keeping the confidence level at 95%, what should they do?

A) 25 ± 0.98

B) 24 ± 0.94

C) 25 ± 0.89

D) 23 ± 0.98

A trivia tournament organizer wanted to study the relationship between the number of points a team scores in a trivia round and the number of hours that a team practices each week. For the study, the organizer selected teams at random from all trivia teams in a certain tournament. The table displays the information for the teams in the sample that practiced for at least hours per week.

Which of the following is the largest population to which the results of the study can be generalized?

$6$

A) The 40 trivia teams in the sample that practiced for at least 3 hours per week.

B) All trivia teams in the tournament.

C) The 55 trivia teams in the sample.

D) All trivia teams in the tournament that scored 14 or more points in the round.

A random sample of 400 town voters were asked if they plan to vote for Candidate A or Candidate B for mayor. The results were sorted by gender and are shown in the table below.

The town has a total of 6,000 voters. Based on the table, what is the best estimate of the number of voters who plan to vote for Candidate A?

$7$

A) 3,550

B) 3,540

C) 3,450

D) 3,570

In a survey conducted in a city with a population of 50,000, a random sample of 500 residents was asked about their preferred mode of transportation to work. Among the sample, 200 residents reported using cars as their primary mode of transportation. What is the estimated number of residents in the city who use cars as their primary mode of transportation to work?

A) 20,100

B) 19,900

C) 20,000

D) 19,800

In a city with a population of 10,000 residents, a survey is conducted to determine the proportion of residents who support a new public transportation initiative. A random sample of 500 residents is taken, and it is found that 250 of them support the initiative.

Based on this sample, estimate the total number of residents in the city who support the new public transportation initiative.

A) 5100

B) 4900

C) 5000

D) 4750

In a survey conducted among 150 members of a fitness club, 60 members indicated that they are interested in participating in a new yoga class. The fitness club has a total membership of 500 members. Based on this survey, estimate how many members in total would be interested in participating in the new yoga class.

A) 190

B) 210

C) 195

D) 200