there were 324 adults surveyed. among the participants, the mean number of hours of sleep each night was 7.5 and the standard deviation was 1.6.

the margin of error, assuming a 95% confidence level, is approximately 0.17. round to the nearest hundredth

the confidence interval is to

Question

there were 324 adults surveyed. among the participants, the mean number of hours of sleep each night was 7.5 and the standard deviation was 1.6.

the margin of error, assuming a 95% confidence level, is approximately 0.17. round to the nearest hundredth

the confidence interval is   to

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Margin of Error Calculation", "Confidence Interval Interpretation" ], "new_concepts": [], "current_concepts": [ "Margin of Error Calculation", "Confidence Interval Interpretation" ] } ## Identify the given values and parameters Using the *Margin of Error Calculation* knowledge point $$ \begin{aligned} &n = 324\ &\bar{x} = 7.5\ &s = 1.6\ &\text{Confidence Level} = 95\% \implies z^* = 1.96\ &\text{Margin of Error } (ME) \approx 0.17 \end{aligned} $$ ## Calculate the confidence interval bounds Using the *Confidence Interval Interpretation* knowledge point $$ \begin{aligned} &\text{Lower Bound} = \bar{x} - ME = 7.5 - 0.17 = 7.33\ &\text{Upper Bound} = \bar{x} + ME = 7.5 + 0.17 = 7.67 \end{aligned} $$ The confidence interval is 7.33 to 7.67. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Statistics", "Confidence Interval Interpretation" ] }

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Identify the given values and parameters

Calculate the confidence interval bounds

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