Question 10 of 10 - Test 3https://assessments.macmill...Completed 10 out of 10ResourcesSubmit AllQuestion 10 of 10A 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 pheromone0.60±0.060.60±0.11.0.60±0.006.0.60±0.14
Q. Question 10 of 10 - Test 3https://assessments.macmill...Completed 10 out of 10ResourcesSubmit AllQuestion 10 of 10A 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 pheromone0.60±0.060.60±0.11.0.60±0.006.0.60±0.14
Identify proportion: Identify the sample proportion.We have 45 insects choosing the pheromone branch out of 75 insects tested.Sample proportion (p^) = Number of successes / Total number of trialsp^=7545=0.60
Calculate SE: Calculate the standard error (SE) of the sample proportion.Standard error formula for proportion: SE=p^(1−p^)/nSE=0.60×(1−0.60)/75SE=0.24/75SE=0.0032SE=0.0566
Determine z-value: Determine the z-value for a 95% confidence level.For a 95% confidence interval, the z-value is approximately 1.96 (from z-tables).z=1.96
Calculate ME: Calculate the margin of error (ME).Margin of error formula: ME=z×SEME=1.96×0.0566ME=0.111