• Part A: This data is from a sample because we are collecting age information for only some of the customers, not all of them.
• Part B: This data is from a population because the community college has information about all students.

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Many people assume the 850 employees is the population because it’s a large number, but this is incorrect. A population includes all members of a group, while specific numbers, like 850, generally refer to a sample.

In this case:

• The 850 employees surveyed represent a sample of the population of all employees at the company.
• The 520 is a statistic calculated from the sample, not the sample itself.

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• Part A: The ecologist wants to study all trees in the forest where birds might build nests. The 1800 trees is misleading because it only represents one part of the forest.
• Part B: The sample is the 300 trees the ecologist selected to observe because samples include only the individuals from whom data is collected.
• Part C: Since the ecologist only observed trees in the northwest region, they can only make inferences about the population of trees in the northwest region, not the entire forest.

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1. The number 706 is a parameter
2. The value $19,856 is a statistic. It would be a parameter by removing "sample of households" and adding "all the households in Tennessee" or "every households in the county": putting in wording that indicates it is a complete collection of households.
3. The percentage 45% is a parameter
4. The value 123.7 is a statistic. This would be a parameter if the "40 different days" was change to "all 365 days of the year" or "all 30 days of this month" to indicate that the voltage measurements are a complete collection.

• Part A: Discrete Quantitative

  The number of pairs of shoes you own is countable (e.g., 1 pair, 2 pairs, 3 pairs, etc.), which makes it quantitative and discrete.

• Part B: Qualitative

  The type of car you drive (e.g., SUV, sedan, truck) is categorical and cannot be measured or counted, making it qualitative data.

• Part C: Continuous Quantitative

  The distance to the nearest grocery store can be measured along a continuous scale (e.g., 1.5 miles, 3.2 miles), allowing for infinite precision, so it is quantitative and continuous.

• Part D: Discrete Quantitative

  The number of classes you take per school year is countable (e.g., 4 classes, 5 classes, etc.), so it is quantitative and discrete.

• Part E: Qualitative

  The type of calculator you use (e.g., graphing calculator, scientific calculator) is descriptive and categorical, making it qualitative data.

• Part F: Continuous Quantitative

  The weights of dogs at an animal shelter can be measured along a continuous scale (e.g., 12.7 pounds, 23.4 pounds) with infinite precision, making this data quantitative and continuous.

• Part G: Discrete Quantitative

  The number of correct answers on a quiz is countable (e.g., 1 correct answer, 2 correct answers), so it is quantitative and discrete.

• Part H: Discrete Quantitative

  Although the amount of money spent at a store can include decimals (e.g., $5.75), money is not measured on a continuous scale because it is typically limited to two decimal places (cents). Thus, it is quantitative and discrete.

• Part A: Categorical data describes attributes or categories and cannot be measured numerically. From the table, the categorical data includes:
  • Make/Model: The names of vehicles, such as "Chevrolet Corvette" or "Nissan Cube."
  • Class: The vehicle category, such as "Two-Seater" or "Midsize."
  • Transmission: The type of transmission, either "Manual" or "Automatic."
  • Cylinders: The number of engine cylinders (e.g., 4, 6, 8) is categorical because it classifies the engine type rather than measuring it.  
• Part B: Quantitative data includes numerical values obtained by counting or measuring. From the table, the quantitative data includes:
  • City MPG: The number of miles per gallon in city driving (e.g., 17, 25, 23, etc.).
  • Highway MPG: The number of miles per gallon in highway driving (e.g., 29, 30, 36, etc.).
  • Annual Fuel Cost: The cost of fuel for one year, measured in dollars (e.g., $2,650, $1,850).

1. Nominal: Types of cars are categorized without order.
2. Ordinal: Rankings in a race indicate an order but do not provide measurable differences between positions.
3. Interval: Fahrenheit temperatures provide measurable differences but lack a true zero.
4. Ratio: Time in seconds includes meaningful differences and a true zero, allowing for ratios.

• Part A: Observational Study: The researchers surveyed respondents and recorded their opinions without imposing any changes or treatments. No variables were manipulated.
• Part B: Experiment: The researchers imposed a treatment by implementing an intensive program to lower systolic blood pressure. They then measured the participants' responses (reduction in the risk of death).

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A single study does not prove a result because of the following issues.

• Any single study is subject to random variation due to chance, as a sample may not perfectly represent the population. This error can cause the results to differ from the true population characteristics purely by chance.
• Without replication, it is difficult to determine whether the observed result is reliable or simply due to random variation. A single study cannot confirm the consistency of findings across repeated experiments.

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The psychologists’ concern about the lack of blindness refers to the fact that the experimenter, who rated the subjects’ anxiety levels both before and after the experiment, knew which group each subject belonged to (meditation or relaxation). This lack of blindness could introduce bias in the following ways:

• The experimenter might have unconsciously expected the meditation group to show greater improvement, leading them to rate that group’s anxiety levels more favorably.
• Since the experimenter knew the treatment assignments, their personal beliefs about meditation's effectiveness could have influenced their ratings, even if unintentionally.

To reduce bias, the experimenter could have implemented a double-blind procedure. In a double-blind experiment,  the experimenter conducting the interviews would not know which group each subject was in. This would ensure that the ratings are based solely on the subjects’ behavior and responses, without being influenced by the experimenter’s expectations.

By using proper blinding, the anxiety ratings would be less likely to reflect the experimenter’s or subjects’ biases, leading to more reliable and unbiased results.

Many people lie in response to this question because voting is socially desirable. People may feel pressure to give an answer that aligns with societal expectations, even if it is not truthful. This is an example of response bias because the respondent’s behavior (lying to conform to expectations) influences the data, making it inaccurate.

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People are more likely to agree with Question A because the phrase "assistance to the poor" evokes a sense of helping those in need. In contrast, the term "welfare" may carry negative connotations for some people, as it is often associated with misuse or dependency. This demonstrates how subtle changes in wording can influence how respondents perceive and answer questions, a key example of wording effects.

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The total number of households contacted was 2000, and the number of responses was 831. To calculate the rate of nonresponse:

\[ \text{Nonresponse Rate} = \dfrac{\text{{Nonresponses}}}{\text{Total Households}} = \dfrac{2000 - 831}{{2000}} = \dfrac{{1169}}{{2000}} = 0.5845 \text{ (or 58.45%)}. \]

The nonresponse rate is 58.45%, which is quite high. The likely reasons include:

• People may not answer calls from unknown numbers or may be busy when called.
• Some people may not feel comfortable sharing personal information, such as how often they go to the movies.
• The question may not seem relevant to everyone, leading to disengagement.

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• Part A: Stratified Sampling: Students are grouped by year and sampled proportionally.
• Part B: Systematic Sampling: A starting point is randomly selected, and every 50th student is chosen.
• Part C: Simple Random Sampling: All students have an equal probability of selection.
• Part D: Cluster Sampling: Entire years are selected, and all students in those years are included.
• Part E: Convenience Sampling: Students are chosen based on availability, leading to potential bias.

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• Part A: Volunteer Response

  The survey link was shared publicly, allowing students to self-select into the sample. This leads to volunteer response bias, as students with strong opinions are more likely to participate, while those with neutral opinions are underrepresented.

• Part B: Nonresponse

  Out of the 1,000 students contacted, only 250 responded, creating nonresponse bias. The opinions of nonrespondents may differ systematically from those of respondents, particularly since frequent diners are overrepresented in the responses.

• Part C: Undercoverage

  The survey was conducted at a single dining hall during lunchtime, excluding students who do not use the dining hall or eat lunch on campus. This undercoverage results in a sample that is not representative of the entire student population.

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The experiment can be modeled using a completely randomized design as follows.

First, we have a block to represent all the individuals in the sample.Next, we randomly sort the individuals into three groups: one group for each treatment and one placebo group. We label the groups 1, 2, and 3. We draw an arrow from our initial block to each of the three groups, as follows.Next, we add a block for each treatment and one for the placebo.  We assign the treatments to the groups at random.  In the diagram, we then draw an arrow from the group to the treatment it receives.  Typically, the treatment block is draw to the right of the group block it is assigned to, as demonstrated in the following image.

Finally, we add a single block at the end indicating that the data is collected, and the results from all the treatment and placebo groups should be compared.  In the flow chart, we indicate this by drawing an arrow from each treatment to the Compare Results box, and our flowchart is complete.

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This experiment uses a randomized block design, and the flowchart can be designed as follows.

As before, we start with a block to represent all the individuals in the sample.

Next, we add in blocks for the different skin types since the creams may affect different skin types differently. We draw an arrow from the sample to each of the different skin types.Now, we treat each block as its own SRS, and assign members in each block into one of two groups, as shown below.Since we are treating each block as its own SRS, we'll assign each group within a block one of the two creams.The whole point of the block design is to account for the different types of skin. So, when we get to the compare results step, we only compare results within each block.  This ensures that any differences observed are due to the treatment and not the characteristics defining the blocks. 

The final flowchart shown below.

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This is a matched-pairs design (Version 2) because each participant serves as their own control by testing both dashboard layouts.  As before, we start off with the random sample.

Next, assign the participants into one of two groups.Next, randomly assign one of the two treatments to each group.After a period of time has passed and under similar conditions, the groups are given the other treatment.Finally, you compute the difference in results between the two treatments, and compare all the differences among the participants.

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