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The scatterplot shows the relationship between two variables, x and y.

Which of the following equations is the most appropriate linear model for the data shown?

A town manager selected 2 random samples of residents in the town to estimate the percentage of all residents that planned to vote in favor of a new business in the downtown area. Based on the first sample, he estimated that 75% of the residents in the town planned to vote in favor; with an associated margin of error of 8.5%.Based on the second sample, he estimated that 83% of the residents in the town planned to vote in favor, with an associated margin of error of 6.9%. Assuming the margins of error were calculated the same way, which of the following best explains why the first sample obtained a larger margin of error than the second sample?

A company studied a random sample of 72 lawns in a small town. The company found that 9 of these lawns contain acidic soil. If there are 1,080 lawns in the town, which of the following is the best estimate of the number of lawns that contain acidic soil?

A district school board in a certain state is proposing a change to the length of lunch periods for all high schools in the district. A sample of 365 high school students was selected at random from all high school students in the district. The selected students were asked whether they approved of the proposed change, and 211 students responded that they did not approve. Which of the following is the largest population to which the results of the survey can be generalized?

A company that produces only one type of item wants to estimate the percent of the items produced in a typical week that are defective. A random sample of 540 of the items produced in a certain week were tested. Based on the sample, it is estimated that 12.5% of all items produced by the company in this week are defective, with an associated margin of error of 2.79%. Based on the estimate and associated margin of error, which of the following is the most appropriate conclusion about all items produced by the company during this week?

A sample was selected at random from a population. Based on the sample, it is estimated that the mean value of a variable for this population is 88, with an associated margin of error of 1.5. Based on the estimate and associated margin of error, which of the following best describes the range of plausible values for the population mean?

For a study, a group of chipmunks will be selected from a habitat consisting of 220 chipmunks, and a group of prairie dogs will be selected from a habitat consisting of 190 prairie dogs. Some of the chipmunks and prairie dogs will be in a treatment group, and some of the chipmunks and prairie dogs will be in a control group. Which of the following is necessary for this study to attempt to establish a cause-and-effect relationship between two variables?

A survey was conducted in Arlington to estimate the percent of adult residents who support the addition of a community pool in their town. Based on the survey, it is estimated that 40% of all adult residents of Arlington support the addition of a community pool in their town, with an associated margin of error of 7%. Which of the following is the most appropriate conclusion about all adult residents of Arlington?

The manager of a gym selected a sample of 142 members at random to estimate the percentage of the gym's members that would continue to pay for a membership if the price increased. From the survey, the manager estimates that 89% of the gym's members would continue to pay for a membership if the price increased, with an associated margin of error of 5.15%. If the survey is repeated with a random sample of 284 members and the results are calculated in the same way, which of the following will be the most likely effect of using the larger random sample compared to the smaller random sample?

For a survey, a sample of 1,018 people was selected at random from all registered voters in a county. Based on the survey, it is estimated that 66% of all registered voters in the county are in favor of a new law, with an associated margin of error of 2.91%. 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 research manager selected 2 random samples of ovens of a certain type to estimate the average amount of time this type of oven takes to preheat to 325 degrees Fahrenheit (°F). The research manager recorded the amount of time, in minutes, each oven takes to preheat to 325 °F. Based on the first sample, the research manager estimated that this type of oven takes an average of 15.2 minutes to preheat to 325 °F, with an associated margin of error of 1 minute. Based on the second sample, the research manager estimated that this type of oven takes an average of 15.4 minutes to preheat to 325 °F, with an associated margin of error of 2.2 minutes. Assuming the margins of error were calculated the same way, which of the following best explains why the first sample obtained a smaller margin of error than the second sample?

A machine fills bags with approximately 11 ounces of walnuts. To test the accuracy of the filling process, 330 bags of walnuts were selected at random and weighed. Based on the sample, it is estimated that the average weight of all bags of walnuts filled by the machine in an 8-hour period is 11.17 ounces, with an associated margin of error of 0.2 ounce. Which of the following is the best interpretation of this estimate?