a survey of 225 students showed the mean number of hours spent studying per week was 20.6 and the standard deviation was 2.7.

assuming a 90% confidence level, the margin of error is approximately 0.3.

which of the following gives the confidence interval?

between 0.07 and 0.13
between 2.4 and 3.1
between 20.3 and 20.9

Question

a survey of 225 students showed the mean number of hours spent studying per week was 20.6 and the standard deviation was 2.7.

assuming a 90% confidence level, the margin of error is approximately 0.3.

which of the following gives the confidence interval?

between 0.07 and 0.13
between 2.4 and 3.1
between 20.3 and 20.9

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Margin of Error Calculation", "Confidence Interval Width" ], "new_concepts": [], "current_concepts": [ "Margin of Error Calculation", "Confidence Interval Width" ] } ## Identify the given parameters Using the *Margin of Error Calculation* knowledge point $$ \begin{aligned} n &= 225 \ \bar{x} &= 20.6 \ s &= 2.7 \ \text{Margin of Error (ME)} &\approx 0.3 \end{aligned} $$ ## Calculate the confidence interval bounds Using the *Confidence Interval Width* knowledge point $$ \begin{aligned} \text{Lower Bound} &= \bar{x} - \text{ME} = 20.6 - 0.3 = 20.3 \ \text{Upper Bound} &= \bar{x} + \text{ME} = 20.6 + 0.3 = 20.9 \end{aligned} $$ ## Match with the correct option The calculated interval is between $20.3$ and $20.9$.

between 0.07 and 0.13

between 2.4 and 3.1

between 20.3 and 20.9

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Statistics", "Confidence Interval Width" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Identify the given parameters

Calculate the confidence interval bounds

Match with the correct option

Answer: