抽样・推断与误差范围

A community organization surveyed a random sample of residents of the community to estimate the percentage of residents who visit their local library at least once per month. From the survey, the organization estimates that 17% of residents of the community visit their local library at least once per month, with an associated margin of error of 3.8%. The organization repeated the survey with a random sample of residents that was double the original sample size. Assuming the margins of error are calculated in the same way for both studies, which of the following is true about the margin of error associated with the estimate from the larger sample?

A biologist recorded the head stripe colors for a random sample of sparrows from a certain population. Each sparrow has either a white-striped head or a tan-striped head. The results are shown in the table.

Based on these results, if there are a total of 686 sparrows in this population, which of the following is the best estimate of how many more sparrows in the population have a tan-striped head than have a white-striped head?

A survey was conducted in Madison to estimate the percent of adult residents who support the addition of a gas station at a popular intersection in their town. Based on the survey, it is estimated that 27% of all adult residents of Madison support the addition of a gas station at a popular intersection in their town, with an associated margin of error of 6%. Which of the following is the most appropriate conclusion about all adult residents of Madison?

A biologist recorded the head stripe colors for a random sample of sparrows from a certain population. Each sparrow has either a white-striped head or a tan-striped head. The results are shown in the table.

Based on these results, if there are a total of 765 sparrows in this population, which of the following is the best estimate of how many more sparrows in the population have a tan-striped head than have a white-striped head?

A researcher surveyed a random sample of 1,380 people from a certain state to estimate the percentage of people who support the governor's recent approval of a bill. From the survey, the researcher estimated that 72% of people from the state support the governor's approval of the bill, with an associated margin of error of 2.37%. The researcher repeated the survey with a random sample of people from the state that was double the original sample size. Assuming the margins of error were calculated in the same way, which of the following is true about the margin of error associated with the estimate from the larger sample?

Four different research groups each surveyed a random sample of students from a certain high school to estimate the percentage of students at the school who speak a second language. The table shows the resulting estimates and their associated margins of error.

Assuming the margins of error were calculated in the same way, which group had the largest sample size?

A machine fills bags with approximately 11 ounces of sugar. To test the accuracy of the filling process, 132 bags of sugar were selected at random and weighed. Based on the sample, it is estimated that the average weight of all bags of sugar filled by the machine in an 8-hour period is 10.83 ounces, with an associated margin of error of 0.2 ounce. Which of the following is the best interpretation of this estimate?

For a survey, a sample of 945 people was selected at random from all registered voters in a county. Based on the survey, it is estimated that 71% of all registered voters in the county are in favor of a new law, with an associated margin of error of 2.89%. Which of the following best describes the plausible values for the percent of all registered voters in the county who are in favor of the new law?

A researcher is designing a study to investigate the average number of hours students at a high school spend reading per day. The researcher will report an estimated average number of hours students at the high school spend reading per day with an associated margin of error. The researcher is considering using a random sample of either 115 or 230 students from the high school. Which of the following would be the most likely effect of using the larger random sample compared to the smaller random sample?

A cable provider wanted to know how many of its 30,000 customers would be interested in a new service plan. The provider selected 300 customers at random and asked each customer whether the customer would be interested in the new plan. Of those surveyed, 8 said they would be interested. Which of the following is the best estimate of the total number of customers who would be interested in the new service plan?

From a population of 50,000 people,1,000 were chosen at random and surveyed about a proposed piece of legislation.Based on the survey, it is estimated that 35% of people in the population support the legislation, with an associated margin of error of 3%. Based on these results, which of the following is a plausible value for the total number of people in the population who support the proposed legislation?

Poll Results

Angel Cruz	483
Terry Smith	320

The table shows the results of a poll. A total of 803 voters selected at random were asked which candidate they would vote for in the upcoming election.According to the poll, if 6,424 people vote in the election, by how many votes would Angel Cruz be expected to win?