In a survey, 1500 adults in a certain country were asked how many hours they worked in the previous week. Based on the results, a 95% confidence interval for mean number of hours worked was lower bound: 39.5 and upper bound: 42.1. Which of the following represents a reasonable interpretation of the result? For those that are not reasonable, explain the flaw. Complete parts (a) through (d) below. (a) There is a 95% chance the mean number of hours worked by adults in this country in the previous week was between 39.5 hours and 42.1 hours. O A. Correct. This interpretation is reasonable. OB. Flawed. This interpretation makes an implication about individuals rather than the mean. OC. Flawed. This interpretation implies that the population mean varies rather than the interval. O D. Flawed. This interpretation implies that the mean is only for last week.

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In a survey, 1500 adults in a certain country were asked how many hours they worked in the previous week. Based on the results, a 95% confidence interval for the mean number of hours worked was established with a lower bound of 39.5 hours and an upper bound of 42.1 hours. The task is to determine which interpretation of the result is reasonable and to identify any flaws in the interpretations given.

Completion of parts (a) through (d) involves assessing the following statement: 

(a) There is a 95% chance the mean number of hours worked by adults in this country in the previous week was between 39.5 hours and 42.1 hours.

- Option A: This interpretation is marked as correct and reasonable.
- Option B: This option is described as flawed because it mistakenly implies something about individuals rather than the overall mean.
- Option C: This option is described as flawed because it incorrectly suggests that the population mean varies instead of being fixed within a given interval.
- Option D: This option is described as flawed because it misleadingly implies that the mean is applicable only to the previous week.
Transcribed Image Text:In a survey, 1500 adults in a certain country were asked how many hours they worked in the previous week. Based on the results, a 95% confidence interval for the mean number of hours worked was established with a lower bound of 39.5 hours and an upper bound of 42.1 hours. The task is to determine which interpretation of the result is reasonable and to identify any flaws in the interpretations given. Completion of parts (a) through (d) involves assessing the following statement: (a) There is a 95% chance the mean number of hours worked by adults in this country in the previous week was between 39.5 hours and 42.1 hours. - Option A: This interpretation is marked as correct and reasonable. - Option B: This option is described as flawed because it mistakenly implies something about individuals rather than the overall mean. - Option C: This option is described as flawed because it incorrectly suggests that the population mean varies instead of being fixed within a given interval. - Option D: This option is described as flawed because it misleadingly implies that the mean is applicable only to the previous week.
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**Transcription for Educational Website:**

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In a survey, 1500 adults in a certain country were asked how many hours they worked in the previous week. Based on the results, a 95% confidence interval for the mean number of hours worked was lower bound: 39.5 and upper bound: 42.1. Which of the following represents a reasonable interpretation of the result? For those that are not reasonable, explain the flaw. Complete parts (a) through (d) below.

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**(a)**

- **A.** Correct. This interpretation is reasonable.
  
- **B.** Flawed. This interpretation makes an implication about individuals rather than the mean.
  
- **C.** ✔️ Flawed. This interpretation implies that the population mean varies rather than the interval.
  
- **D.** Flawed. This interpretation implies that the mean is only for last week.

---

**(b)** We are 95% confident that the mean number of hours worked by adults in this country in the previous week was between 39.5 hours and 42.1 hours.

- **A.** Flawed. This interpretation makes an implication about individuals rather than the mean.
  
- **B.** Correct. This interpretation is reasonable.
  
- **C.** Flawed. This interpretation implies that the population mean varies rather than the interval.
  
- **D.** Flawed. This interpretation does not make it clear that the 95% is the probability that the mean is within the interval.

---

**Explanation of the Diagrams:**

- The given image contains multiple-choice sections (a) and (b), where each section evaluates interpretations of a confidence interval result. 
- Each option is marked as either correct or flawed with a brief explanation of why it is reasonable or what the specific flaw is. The selected correct answer for each section is indicated by a check mark (✔️).

---
Transcribed Image Text:**Transcription for Educational Website:** --- In a survey, 1500 adults in a certain country were asked how many hours they worked in the previous week. Based on the results, a 95% confidence interval for the mean number of hours worked was lower bound: 39.5 and upper bound: 42.1. Which of the following represents a reasonable interpretation of the result? For those that are not reasonable, explain the flaw. Complete parts (a) through (d) below. --- **(a)** - **A.** Correct. This interpretation is reasonable. - **B.** Flawed. This interpretation makes an implication about individuals rather than the mean. - **C.** ✔️ Flawed. This interpretation implies that the population mean varies rather than the interval. - **D.** Flawed. This interpretation implies that the mean is only for last week. --- **(b)** We are 95% confident that the mean number of hours worked by adults in this country in the previous week was between 39.5 hours and 42.1 hours. - **A.** Flawed. This interpretation makes an implication about individuals rather than the mean. - **B.** Correct. This interpretation is reasonable. - **C.** Flawed. This interpretation implies that the population mean varies rather than the interval. - **D.** Flawed. This interpretation does not make it clear that the 95% is the probability that the mean is within the interval. --- **Explanation of the Diagrams:** - The given image contains multiple-choice sections (a) and (b), where each section evaluates interpretations of a confidence interval result. - Each option is marked as either correct or flawed with a brief explanation of why it is reasonable or what the specific flaw is. The selected correct answer for each section is indicated by a check mark (✔️). ---
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