Question 1

Conduct a survey to determine the major worry of school teachers.

Accepted Answer

To conduct a survey to determine the major worry of school teachers, we would first need to create a survey questionnaire that includes questions about various potential worries that teachers may have. These could include concerns about student behavior, workload, administrative support, resources and materials, student performance, and job security. We would then distribute the survey to a representative sample of school teachers and analyze the results to determine which worries are most prevalent among teachers. This information could then be used to address and alleviate the major worries of school teachers in order to improve their overall well-being and job satisfaction.

Question 2

An alpinism club would like to survey its members to determine where to go next summer. ​
Decide on a reasonable means for conducting the survey to obtain the desired information.
​

Accepted Answer

The most reasonable means for determining where the club should go next summer would be to survey the members of the alpinism club. They are the ones with the experience and interest in this area, and their input would be the most valuable. Conducting a survey of random people would not necessarily provide relevant responses, as they may not have the experience or interest in alpinism. Additionally, surveying random people on the street or from a telephone directory could provide biased results, as they may not represent the typical alpinism club member.

Question 3

Conduct a survey to determine whether there is a significant correlation between history scores in the 6th grade and amount of TV viewing.

Accepted Answer

To conduct a survey to determine whether there is a significant correlation between history scores in the 6th grade and the amount of TV viewing, you would need to follow these steps:

1. **Define the Hypothesis**: 
   - Null Hypothesis (H0): There is no significant correlation between history scores in the 6th grade and the amount of TV viewing.
   - Alternative Hypothesis (H1): There is a significant correlation between history scores in the 6th grade and the amount of TV viewing.

2. **Identify the Population and Sample**:
   - The population could be all 6th-grade students in a particular region or school district.
   - The sample should be a representative subset of that population. You might use random sampling or stratified sampling to ensure diversity and representativeness.

3. **Develop a Survey Instrument**:
   - Create a questionnaire that asks about the amount of TV viewing per day/week and collects data on history scores. Ensure questions are clear and unbiased.
   - Include demographic questions to control for potential confounding variables (e.g., age, gender, socioeconomic status).

4. **Pilot the Survey**:
   - Test the survey on a small group of students to check for understanding and to ensure that the questions measure what they are intended to measure.

5. **Administer the Survey**:
   - Distribute the survey to the sample of 6th-grade students. This could be done in person, by mail, or online, depending on resources and access.

6. **Collect Data**:
   - Gather the completed surveys and organize the data for analysis. Ensure that all data is kept confidential and that participants' anonymity is maintained.

7. **Analyze the Data**:
   - Use statistical software or methods to analyze the data. A Pearson correlation coefficient could be calculated to determine the strength and direction of the relationship between TV viewing and history scores.
   - Conduct a regression analysis if you want to control for other variables.

8. **Interpret the Results**:
   - Determine if the correlation is statistically significant (typically, a p-value of less than 0.05 is considered significant).
   - Consider the size of the correlation coefficient to understand the strength of the relationship.

9. **Report the Findings**:
   - Prepare a report or presentation that summarizes the methodology, analysis, and findings.
   - Discuss whether the results support the null hypothesis or the alternative hypothesis.

10. **Consider Ethical Implications**:
    - Ensure that the survey complies with ethical standards, including informed consent, confidentiality, and the right to withdraw.

11. **Reflect on Limitations**:
    - Acknowledge any limitations of the study, such as sample size, response bias, or other factors that could affect the validity of the results.

12. **Make Recommendations**:
    - Based on the findings, make recommendations for educators, parents, or policymakers. If a significant correlation is found, suggest possible interventions or further research.

Remember that correlation does not imply causation. Even if a significant correlation is found, it does not mean that TV viewing causes changes in history scores or vice versa. Other factors could be influencing both variables.

Question 4

Suppose that of 80 workers randomly selected and interviewed, 53 were opposed to an increase in Social Security taxes. Would you accept or reject the hypothesis that the majority of workers are opposed to the increase in taxes? ​

Accepted Answer

The sample size is large enough to use the normal distribution to approximate the binomial distribution. The sample proportion of workers opposed to the increase in taxes is 53/80 = 0.6625. The standard deviation of the sample proportion is sqrt(0.6625 * 0.3375 / 80) = 0.0433. The z-score for the sample proportion is (0.6625 - 0.5) / 0.0433 = 3.78. The p-value for the z-score is less than 0.0001, which is less than the significance level of 0.05. Therefore, we reject the hypothesis that the majority of workers are opposed to the increase in taxes.

Question 5

The government wants to use a survey to determine the extent of public approval for a adopting new rules of getting the driving license. ​
Decide on a reasonable means for conducting the survey to obtain the desired information.
​

Accepted Answer

Surveying as many inhabitants as possible will provide a larger sample size and a more representative result than any of the other options. Randomly choosing inhabitants of a neighboring country would not be relevant to the population in question, surveying only students of a local college would not represent the general public, and asking the opinion of only four individuals would not provide enough data. Asking the opinion of retired professors or inhabitants may provide some valuable insight, but it may not be representative of the entire population. Therefore, option B is the best choice for conducting the survey.

Question 6

The government wants to use a survey to determine the extent of public approval for a adopting new rules of getting the driving license.
​
Decide on a reasonable means for conducting the survey to obtain the desired information.

Accepted Answer

The answer of The government wants to use a survey...

Question 7

An environmental group wants to use a survey to determine the extent to which its members would be willing to protest a recent decision of the governor of a particular state. Which of the following procedures would be most appropriate for obtaining a statistically unbiased sample? ​

Accepted Answer

The best choice for obtaining a statistically unbiased sample would be to survey a selection of people whose names are randomly chosen from a list of members of the environmental group, as this would ensure that only members of the group who are interested in environmental issues are included in the survey. Surveying people from the telephone directory or sign-ups at local malls may include individuals who are not interested in environmental issues, and surveying only members attending the annual convention may not be representative of the views of all members of the group.

Question 8

A pet store would like to use a survey to determine which factors are most important to cat owners in determining the brand of cat food that they purchase. ​
Decide on a reasonable means for conducting the survey to obtain the desired information.
​

Accepted Answer

Surveying 1000 cat keepers by randomly choosing from a list of pet keepers is the best choice as it ensures that the respondents are all cat owners and are thus relevant to the survey. Option A only surveys persons from the local telephone directory, which may not include cat owners. Option C surveys random people who may not even have a cat as a pet. Option D may also survey people who do not own cats. Therefore, option B is the most reasonable means of conducting the survey.

Question 9

Krispy Kreme is considering building a franchise in a particular city. It will use a survey to determine the extent of interest among residents of the city. Which of the following procedures would be most appropriate for obtaining a statistically unbiased sample?

Accepted Answer

Surveying a selection of people who are listed on the residential roll sheets of the city allows for a more representative and unbiased sample of the city's population, as it does not pre-select individuals based on specific behaviors or interests.

Question 10

A movie theater would like to use a survey to determine which factors are most important to those who come to their theater. Which of the following procedures would be most appropriate for obtaining a statistically unbiased sample? ​

Accepted Answer

The most appropriate procedure would be to survey a random selection of people who are leaving the theater after watching a movie. This way, the sample is more likely to consist of people who have actually been to the theater and are therefore most knowledgeable about the factors that may be important to them. Sampling people leaving the theater also allows the survey to capture the moviegoing experience in its entirety, rather than relying on people's memories or perceptions of the theater.

Question 11

Conduct a survey to determine whether there is a significant correlation between math scores in the 8th grade and amount of listening to the radio.

Accepted Answer

The survey questions in choice E directly relate to the research question of whether there is a correlation between 8th grade math scores and the amount of time spent listening to the radio. The other survey questions do not relate to the research question and would not provide relevant data.

Question 12

A pet store would like to use a survey to determine which factors are most important to cat owners in determining the brand of cat food that they purchase.
​
Decide on a reasonable means for conducting the survey to obtain the desired information.

Accepted Answer

The answer of A pet store would like to use...

Question 13

A community will use a survey to determine if its members approve of a new charter.
​
Decide on a reasonable means for conducting the survey to obtain the desired information.

Accepted Answer

The answer of A community will use a survey to...

Question 14

Suppose that John hands you a coin to flip and wants to bet on the outcome. Now, John has tried this sort of thing before, and you suspect that the coin is "rigged." You decide to test this hypothesis by taking a sample. You flip the coin twice, and it is heads both times. You say, "Aha, I knew it was rigged!" John replies, "Don't be silly. Any coin can come up heads twice in a row." ​
The following scheme was devised to allow fair results even if the coin is somewhat biased. The coin is flipped twice. If it comes up heads both times or tails both times, it is flipped twice again. If it comes up heads-tails, this will decide the outcome in favor of the first party; and if it comes up tails-heads, this will decide the outcome in favor of the second party. Will this result in a fair toss even if the coins are biased?
​

Accepted Answer

This scheme will result in a fair toss even if the coins are biased. This is because if the coin is biased towards heads, for example, the probability of getting heads-heads or tails-tails in the first two tosses is higher, but if that happens, the coin is flipped again until either heads-tails or tails-heads appear, which has an equal probability of 1/2. Therefore, the overall probability of either party winning is 1/2, which is a fair toss.

Question 15

Sprint would like to take customers from Pacific Bell, one of its competitors in a certain geographical area. Sprint would like to survey Pacific Bell's customers in order to find out which elements of its service are least satisfactory. Which of the following procedures would be most appropriate for obtaining a statistically unbiased sample? ​

Accepted Answer

The most appropriate procedure for obtaining a statistically unbiased sample would be to survey a random selection of people chosen from a list of Pacific Bell's customers. This ensures that the sample represents the population being studied and reduces the risk of selection bias. Option B is not appropriate because it will not provide information about Pacific Bell's customers. Option C may lead to self-selection bias because people who respond to the advertisement may not be representative of Pacific Bell's customer population. Option D may lead to bias because people who answer the phone may not be representative of Pacific Bell's customer population.

Question 16

A movie theater would like to use a survey to determine which factors are most important to those who come to their theater. Which of the following procedures would be most appropriate for obtaining a statistically unbiased sample? ​

Accepted Answer

Surveying a random selection of people who are leaving the theater after watching a movie would be the most appropriate option as it targets the population of interest (people who come to their theater). Surveying shoppers in the mall or people passing by the theater may not accurately represent this population, while inducing people to answer the survey with discounts may introduce bias in the sample.

Question 17

Sprint would like to take customers from Pacific Bell, one of its competitors in a certain geographical area. Sprint would like to survey Pacific Bell's customers in order to find out which elements of its service are least satisfactory. What procedure would be most appropriate for obtaining a statistically unbiased sample?

Accepted Answer

The answer of Sprint would like to take customers from...

Question 18

Conduct a survey to determine the major worry of school teachers.

Accepted Answer

The questions in option A are geared towards identifying the major worry of school teachers and probing their reasons for feeling worried.

Answer: B and C
 The questions in options B and C are not relevant to determining the major worry of school teachers.

Answer: D
 While the questions in option D are somewhat relevant to school teachers, they do not directly address their major worry.

Answer: E and A
 The questions in option E are somewhat relevant to school teachers, but they are not as direct as those in option A. Therefore, the best choice would be a combination of options E and A.

Question 19

Suppose that John hands you a coin to flip and wants to bet on the outcome. Now, John has tried this sort of thing before, and you suspect that the coin is "rigged." You decide to test this hypothesis by taking a sample. You flip the coin twice, and it is heads both times. You say, "Aha, I knew it was rigged!" John replies, "Don't be silly. Any coin can come up heads twice in a row."
​
The following scheme was devised by mathematician John von Neumann to allow fair results even if the coin is somewhat biased. The coin is flipped twice. If it comes up heads both times or tails both times, it is flipped twice again. If it comes up heads-tails, this will decide the outcome in favor of the first party; and if it comes up tails-heads, this will decide the outcome in favor of the second party. Show that this will result in a fair toss even if the coins are biased.

Accepted Answer

The answer of Suppose that John hands you a coin...

Question 20

Suppose that of 80 workers randomly selected and interviewed, 47 were opposed to an increase in Social Security taxes. Would you accept or reject the hypothesis that the majority of workers are opposed to the increase in taxes?
​
It will be correct to __________ (accept, reject) the hypothesis.

Accepted Answer

The answer of Suppose that of 80 workers randomly selected...

Quiz 14: The Nature of Statistics

Conduct a survey to determine the major worry of school teachers.

An alpinism club would like to survey its members to determine where to go next summer. Decide on a reasonable means for conducting the survey to obtain the desired information.

Conduct a survey to determine whether there is a significant correlation between history scores in the 6th grade and amount of TV viewing.

Suppose that of 80 workers randomly selected and interviewed, 53 were opposed to an increase in Social Security taxes. Would you accept or reject the hypothesis that the majority of workers are opposed to the increase in taxes?

The government wants to use a survey to determine the extent of public approval for a adopting new rules of getting the driving license. Decide on a reasonable means for conducting the survey to obtain the desired information.

The government wants to use a survey to determine the extent of public approval for a adopting new rules of getting the driving license. Decide on a reasonable means for conducting the survey to obtain the desired information.

An environmental group wants to use a survey to determine the extent to which its members would be willing to protest a recent decision of the governor of a particular state. Which of the following procedures would be most appropriate for obtaining a statistically unbiased sample?

A pet store would like to use a survey to determine which factors are most important to cat owners in determining the brand of cat food that they purchase. Decide on a reasonable means for conducting the survey to obtain the desired information.

Krispy Kreme is considering building a franchise in a particular city. It will use a survey to determine the extent of interest among residents of the city. Which of the following procedures would be most appropriate for obtaining a statistically unbiased sample?

A movie theater would like to use a survey to determine which factors are most important to those who come to their theater. Which of the following procedures would be most appropriate for obtaining a statistically unbiased sample?

Conduct a survey to determine whether there is a significant correlation between math scores in the 8th grade and amount of listening to the radio.

A pet store would like to use a survey to determine which factors are most important to cat owners in determining the brand of cat food that they purchase. Decide on a reasonable means for conducting the survey to obtain the desired information.

A community will use a survey to determine if its members approve of a new charter. Decide on a reasonable means for conducting the survey to obtain the desired information.

A movie theater would like to use a survey to determine which factors are most important to those who come to their theater. Which of the following procedures would be most appropriate for obtaining a statistically unbiased sample?

Conduct a survey to determine the major worry of school teachers.

Suppose that of 80 workers randomly selected and interviewed, 47 were opposed to an increase in Social Security taxes. Would you accept or reject the hypothesis that the majority of workers are opposed to the increase in taxes? It will be correct to __________ (accept, reject) the hypothesis.

Quiz 14: The Nature of Statistics

Conduct a survey to determine the major worry of school teachers.

An alpinism club would like to survey its members to determine where to go next summer. ​ Decide on a reasonable means for conducting the survey to obtain the desired information. ​

Conduct a survey to determine whether there is a significant correlation between history scores in the 6th grade and amount of TV viewing.

Suppose that of 80 workers randomly selected and interviewed, 53 were opposed to an increase in Social Security taxes. Would you accept or reject the hypothesis that the majority of workers are opposed to the increase in taxes? ​

The government wants to use a survey to determine the extent of public approval for a adopting new rules of getting the driving license. ​ Decide on a reasonable means for conducting the survey to obtain the desired information. ​

The government wants to use a survey to determine the extent of public approval for a adopting new rules of getting the driving license. ​ Decide on a reasonable means for conducting the survey to obtain the desired information.

An environmental group wants to use a survey to determine the extent to which its members would be willing to protest a recent decision of the governor of a particular state. Which of the following procedures would be most appropriate for obtaining a statistically unbiased sample? ​

A pet store would like to use a survey to determine which factors are most important to cat owners in determining the brand of cat food that they purchase. ​ Decide on a reasonable means for conducting the survey to obtain the desired information. ​

Krispy Kreme is considering building a franchise in a particular city. It will use a survey to determine the extent of interest among residents of the city. Which of the following procedures would be most appropriate for obtaining a statistically unbiased sample?

A movie theater would like to use a survey to determine which factors are most important to those who come to their theater. Which of the following procedures would be most appropriate for obtaining a statistically unbiased sample? ​

Conduct a survey to determine whether there is a significant correlation between math scores in the 8th grade and amount of listening to the radio.

A pet store would like to use a survey to determine which factors are most important to cat owners in determining the brand of cat food that they purchase. ​ Decide on a reasonable means for conducting the survey to obtain the desired information.

A community will use a survey to determine if its members approve of a new charter. ​ Decide on a reasonable means for conducting the survey to obtain the desired information.

A movie theater would like to use a survey to determine which factors are most important to those who come to their theater. Which of the following procedures would be most appropriate for obtaining a statistically unbiased sample? ​

Conduct a survey to determine the major worry of school teachers.

Suppose that of 80 workers randomly selected and interviewed, 47 were opposed to an increase in Social Security taxes. Would you accept or reject the hypothesis that the majority of workers are opposed to the increase in taxes? ​ It will be correct to __________ (accept, reject) the hypothesis.

An alpinism club would like to survey its members to determine where to go next summer. Decide on a reasonable means for conducting the survey to obtain the desired information.

Suppose that of 80 workers randomly selected and interviewed, 53 were opposed to an increase in Social Security taxes. Would you accept or reject the hypothesis that the majority of workers are opposed to the increase in taxes?

The government wants to use a survey to determine the extent of public approval for a adopting new rules of getting the driving license. Decide on a reasonable means for conducting the survey to obtain the desired information.

The government wants to use a survey to determine the extent of public approval for a adopting new rules of getting the driving license. Decide on a reasonable means for conducting the survey to obtain the desired information.

An environmental group wants to use a survey to determine the extent to which its members would be willing to protest a recent decision of the governor of a particular state. Which of the following procedures would be most appropriate for obtaining a statistically unbiased sample?

A pet store would like to use a survey to determine which factors are most important to cat owners in determining the brand of cat food that they purchase. Decide on a reasonable means for conducting the survey to obtain the desired information.

A movie theater would like to use a survey to determine which factors are most important to those who come to their theater. Which of the following procedures would be most appropriate for obtaining a statistically unbiased sample?

A pet store would like to use a survey to determine which factors are most important to cat owners in determining the brand of cat food that they purchase. Decide on a reasonable means for conducting the survey to obtain the desired information.

A community will use a survey to determine if its members approve of a new charter. Decide on a reasonable means for conducting the survey to obtain the desired information.

A movie theater would like to use a survey to determine which factors are most important to those who come to their theater. Which of the following procedures would be most appropriate for obtaining a statistically unbiased sample?

Suppose that of 80 workers randomly selected and interviewed, 47 were opposed to an increase in Social Security taxes. Would you accept or reject the hypothesis that the majority of workers are opposed to the increase in taxes? It will be correct to __________ (accept, reject) the hypothesis.