State whether the data described below are discrete or continuous, and explain why. The number of people in a theater each night Choose the correct answer below. O A. The data are continuous because the data can only take on specific values. O B. The data are discrete because the data can only take on specific values.

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**Title: Understanding Discrete vs. Continuous Data**

**Question:**
State whether the data described below are discrete or continuous, and explain why.

**Scenario:** 
The number of people in a theater each night.

**Options:**

- **A.** The data are continuous because the data can only take on specific values.
- **B.** The data are discrete because the data can only take on specific values.
- **C.** The data are continuous because the data can take on any value in an interval.
- **D.** The data are discrete because the data can take on any value in an interval.

**Explanation:**

In this scenario, you are asked to determine if the "number of people in a theater each night" is an example of discrete or continuous data.

- **Discrete Data:** Represents items that can be counted in whole numbers. These data points cannot be subdivided meaningfully. For example, the number of people can be counted as whole numbers (e.g., 1, 2, 3).

- **Continuous Data:** Represents measurements and can take on any value within a given range. These data points can be split into smaller parts. For example, height or temperature can take on a continuous spectrum of values.

**Correct Answer:**

- **B.** The data are discrete because the data can only take on specific values.

The number of people in a theater each night is discrete because it can only be a whole number. You cannot have a fraction of a person, hence the data can only take specific, whole number values.
Transcribed Image Text:**Title: Understanding Discrete vs. Continuous Data** **Question:** State whether the data described below are discrete or continuous, and explain why. **Scenario:** The number of people in a theater each night. **Options:** - **A.** The data are continuous because the data can only take on specific values. - **B.** The data are discrete because the data can only take on specific values. - **C.** The data are continuous because the data can take on any value in an interval. - **D.** The data are discrete because the data can take on any value in an interval. **Explanation:** In this scenario, you are asked to determine if the "number of people in a theater each night" is an example of discrete or continuous data. - **Discrete Data:** Represents items that can be counted in whole numbers. These data points cannot be subdivided meaningfully. For example, the number of people can be counted as whole numbers (e.g., 1, 2, 3). - **Continuous Data:** Represents measurements and can take on any value within a given range. These data points can be split into smaller parts. For example, height or temperature can take on a continuous spectrum of values. **Correct Answer:** - **B.** The data are discrete because the data can only take on specific values. The number of people in a theater each night is discrete because it can only be a whole number. You cannot have a fraction of a person, hence the data can only take specific, whole number values.
In a study designed to test the effectiveness of a medication as a treatment for lower back pain, 1643 patients were randomly assigned to one of three groups: 
1. The 547 subjects in the placebo group were given pills containing no medication. 
2. 550 subjects were in a group given pills with the medication taken at regular intervals. 
3. 546 subjects were in a group given pills with the medication to be taken when needed for pain relief. 

In what specific way was replication applied in the study?

Choose the correct answer below.

- A. The researchers did not know whether the subjects in the study were taking a placebo or the medication.
- B. The group sample sizes are all large so the researchers could see the effects of the treatment.
- C. The subjects were divided into three groups so the researchers could compare the effects of the different treatments.
- D. The subjects in the study did not know whether they were taking a placebo or the medication.
Transcribed Image Text:In a study designed to test the effectiveness of a medication as a treatment for lower back pain, 1643 patients were randomly assigned to one of three groups: 1. The 547 subjects in the placebo group were given pills containing no medication. 2. 550 subjects were in a group given pills with the medication taken at regular intervals. 3. 546 subjects were in a group given pills with the medication to be taken when needed for pain relief. In what specific way was replication applied in the study? Choose the correct answer below. - A. The researchers did not know whether the subjects in the study were taking a placebo or the medication. - B. The group sample sizes are all large so the researchers could see the effects of the treatment. - C. The subjects were divided into three groups so the researchers could compare the effects of the different treatments. - D. The subjects in the study did not know whether they were taking a placebo or the medication.
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