Exam 7: Survey Sampling and Inference

Suppose that Michigan lawmakers survey 500 randomly selected registered voters to see if they favor an extension of the fall duck hunting season. The lawmakers believe the population proportion in favor of extending the duck hunting season is 45% (based on historical data and previous votes). State the three conditions of the Central Limit Theorem and explain whether each condition is satisfied in this scenario.

Confidence intervals can be used to determine whether different sample proportions reflect a "real" difference in the population. The basic approach is to

Suppose that in a recent poll of 900 adults between the ages of 35 and 45, 22% surveyed said they have thought about participating in an extreme sport such as bungee jumping. Find the 95% confidence interval for the proportion of adults ages 35 to 45 who have thought about participating in an extreme sport such as bungee jumping then choose the correct interpretation. (Round to the nearest tenth of a percent)

The mean age of all the U. S. vice presidents when they took office would be a .

Suppose a city manager conducts a poll and finds that a 95% confidence interval for the proportion of residents who support parking restrictions during snow removal periods as 63% to 71%. Explain what this confidence interval means - the 95% and what the interval represents.

Suppose the event planner assumes that 2.8% of the children attending the event will be lactose intolerant so he orders 7 lactose-free meals. What is the approximate probability that more than 2.8% of the children attending the event are lactose intolerant and that he will not have enough lactose-free meals? Round to the nearest thousandth.

Use the following information to answer questions (14)-(15). In a recent poll of 1100 randomly selected home delivery truck drivers, 26% said they had encountered an aggressive dog on the job at least once. -What is the standard error for the estimate of the proportion of all home delivery truck drivers who have encountered an aggressive dog on the job at least once? Round to the nearest ten-thousandth.

According to the manufacturer of the candy Skittles, 25% of the candy produced are green. If we take a random sample of 10 bags of Skittles, what is the probability that the proportion in our sample of green candies will be more than 25%? Which statement, if any, is true for the conditions to use the Central Limit Theorem?

Use the following information to answer questions (15)-(16). In a recent poll of 900 randomly selected adults, 37% reported that they could not swim 24 yards (the length of a typical gymnasium lap pool). -Report the 95% confidence interval for the proportion of adults who self-report that they cannot swim 24 yards. Round final calculations to the nearest tenth of a percent.

The bias of is zero if certain conditions are met. Identify which condition is not required.

Explain the difference between a population and a sample. Give an example of each.

A group of battery powered toys produced in a day at a factory has a defect rate of 0.5%. Suppose a quality inspector randomly inspects 200 of the toys. Complete the following statement: The quality inspector should expect ____defective toys, with an error of ____.

Complete the statement by filling in the blank. When constructing a confidence interval, if the level of confidence decreases, the margin of error will and the confidence interval will be .

Explain the difference between the standard error of a sample proportion and the margin of error of a confidence interval for a population proportion.

There are five colors available in each bag of Skittles. It is known that the 18% of the Skittles are red. On average, how many Skittles from a random sample of 40 (with replacement) would be expected to be red? Round to the nearest whole Skittle.

Confidence intervals can be used to determine whether different sample proportions reflect a "real" difference in the population. Explain the method of how this is accomplished and what the assumptions are.

Suppose the event planner assumes that only 0.8% of the children attending the event will be lactose intolerant so he orders 2 lactose-free meals. What is the approximate probability that he will have too many lactose-free meals? Round to the nearest thousandth.

If it is being used to make inferences about a population, a good statistic (or estimator) should

Explain the difference between a statistic and a parameter. Give an example of each.

Researchers are interested in learning more about the age of men when they marry for the first time so they survey 500 married or divorced men and ask them how old they were when they first married. The mean age of the 500 men when they married for the first time would be a .