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Question 10 of 10 - Test 3
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Question 10 of 10
A forced-choice design is often used to compare the attractiveness of pheromones to insects. A Y-tube is us is placed on one branch, the control on the second branch, and the insect on the third branch. The insect the two branches. Suppose that 45 of 75 insects choose the pheromone branch.
The 
95% large-sample confidence interval for the proportion of the population that prefers the pheromone

0.60+-0.06

0.60+-0.11.

0.60+-0.006.

0.60+-0.14

Question 1010 of 1010 - Test 33\newlinehttps://assessments.macmill...\newlineCompleted 1010 out of 1010\newlineResources\newlineSubmit All\newlineQuestion 1010 of 1010\newlineA forced-choice design is often used to compare the attractiveness of pheromones to insects. A Y-tube is us is placed on one branch, the control on the second branch, and the insect on the third branch. The insect the two branches. Suppose that 4545 of 7575 insects choose the pheromone branch.\newlineThe 95% 95 \% large-sample confidence interval for the proportion of the population that prefers the pheromone\newline0.60±0.06 0.60 \pm 0.06 \newline0.60±0.11 0.60 \pm 0.11 .\newline0.60±0.006 0.60 \pm 0.006 .\newline0.60±0.14 0.60 \pm 0.14

Full solution

Q. Question 1010 of 1010 - Test 33\newlinehttps://assessments.macmill...\newlineCompleted 1010 out of 1010\newlineResources\newlineSubmit All\newlineQuestion 1010 of 1010\newlineA forced-choice design is often used to compare the attractiveness of pheromones to insects. A Y-tube is us is placed on one branch, the control on the second branch, and the insect on the third branch. The insect the two branches. Suppose that 4545 of 7575 insects choose the pheromone branch.\newlineThe 95% 95 \% large-sample confidence interval for the proportion of the population that prefers the pheromone\newline0.60±0.06 0.60 \pm 0.06 \newline0.60±0.11 0.60 \pm 0.11 .\newline0.60±0.006 0.60 \pm 0.006 .\newline0.60±0.14 0.60 \pm 0.14
  1. Identify proportion: Identify the sample proportion.\newlineWe have 4545 insects choosing the pheromone branch out of 7575 insects tested.\newlineSample proportion (p^\hat{p}) = Number of successes / Total number of trials\newlinep^=4575=0.60\hat{p} = \frac{45}{75} = 0.60
  2. Calculate SE: Calculate the standard error (SE) of the sample proportion.\newlineStandard error formula for proportion: SE=p^(1p^)/nSE = \sqrt{\hat{p}(1 - \hat{p}) / n}\newlineSE=0.60×(10.60)/75SE = \sqrt{0.60 \times (1 - 0.60) / 75}\newlineSE=0.24/75SE = \sqrt{0.24 / 75}\newlineSE=0.0032SE = \sqrt{0.0032}\newlineSE=0.0566SE = 0.0566
  3. Determine z-value: Determine the z-value for a 9595% confidence level.\newlineFor a 9595% confidence interval, the z-value is approximately 1.961.96 (from z-tables).\newlinez=1.96z = 1.96
  4. Calculate ME: Calculate the margin of error (ME).\newlineMargin of error formula: ME=z×SEME = z \times SE\newlineME=1.96×0.0566ME = 1.96 \times 0.0566\newlineME=0.111ME = 0.111
  5. Construct interval: Construct the confidence interval.\newlineConfidence interval formula: p^±ME\hat{p} \pm \text{ME}\newlineConfidence interval = 0.60±0.1110.60 \pm 0.111

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