Question

an ice cream company surveyed 1000 random individuals to see if they prefer chocolate or vanilla ice cream. of those surveyed, 550 preferred chocolate. the ice cream company simulated the survey and found the margin of error to be 40. what does the margin of error mean in relation to this survey? move numbers to the blanks to complete the sentence. the population mean for individuals preferring chocolate is estimated as being a value within the interval of __ to because __ % of the sample means from the simulation trials fell within this interval. 40 55 95 510 550 530 570 590

Explanation:

Step1: Find the lower bound

The sample proportion (or in this case, the number of people who preferred chocolate) is 550. The margin of error is 40. To find the lower bound of the interval, we subtract the margin of error from the sample value: \(550 - 40 = 510\).

Step2: Find the upper bound

To find the upper bound of the interval, we add the margin of error to the sample value: \(550 + 40 = 590\).

Step3: Determine the percentage

In a typical sampling distribution, approximately 95% of the sample means (or in this case, sample counts) fall within the interval around the population mean (estimated by the sample) that is calculated using the margin of error. So the percentage is 95.

Answer:

The population mean for individuals preferring chocolate is estimated as being a value within the interval of \(510\) to \(590\) because \(95\) % of the sample means from the simulation trials fell within this interval.