you are the operations manager for an airline and you are considering a higher fare level for passengers in aisle seats. how many randomly selected air passengers must you survey? assume that you want to be 90% confident that the sample percentage is within 5.5 percentage points of the true population percentage. complete parts (a) and (b) below.

a. assume that nothing is known about the percentage of passengers who prefer aisle seats.
$n = 224$
(round up to the nearest integer.)

b. assume that a prior survey suggests that about 36% of air passengers prefer an aisle seat.
$n = $
(round up to the nearest integer.)

Question

you are the operations manager for an airline and you are considering a higher fare level for passengers in aisle seats. how many randomly selected air passengers must you survey? assume that you want to be 90% confident that the sample percentage is within 5.5 percentage points of the true population percentage. complete parts (a) and (b) below.

a. assume that nothing is known about the percentage of passengers who prefer aisle seats.
$n = 224$
(round up to the nearest integer.)

b. assume that a prior survey suggests that about 36% of air passengers prefer an aisle seat.
$n = $
(round up to the nearest integer.)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Sample Size for Proportions" ], "new_concepts": [], "current_concepts": [ "Sample Size for Proportions", "Margin of Error for Proportions" ] } ## Identify given parameters and critical value $$ \begin{aligned} &E = 0.055\ &\text{Confidence Level} = 0.90 \implies \alpha = 0.10 \implies z_{\alpha/2} = z_{0.05} \approx 1.645\ &\hat{p} = 0.36,\quad \hat{q} = 1 - \hat{p} = 0.64 \end{aligned} $$ ## Calculate minimum sample size $$ \begin{aligned} n &= \frac{(z_{\alpha/2})^2 \cdot \hat{p} \cdot \hat{q}}{E^2}\ n &= \frac{(1.645)^2 \cdot 0.36 \cdot 0.64}{(0.055)^2}\ n &= \frac{2.706025 \cdot 0.2304}{0.003025}\ n &\approx \frac{0.62346816}{0.003025} \approx 206.105 \end{aligned} $$ ## Round up to the nearest integer $$ n = \lceil 206.105 ceil = 207 $$ b. Assume that a prior survey suggests that about 36% of air passengers prefer an aisle seat. $n =$ 207 (Round up to the nearest integer.) { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Statistics", "Sample Size for Proportions" ] }

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Question

Explanation:

Identify given parameters and critical value

Calculate minimum sample size

Round up to the nearest integer

Answer: