Inference

There are 400 students at Polly's school. She surveyed a random sample of 80 students to find their favorite hobby. 19 said they like to read. 30 said they like to be with friends. 8 said they like to do crafts. 23 said they like to play sports. Polly infers that doing crafts is the least popular hobby at her school. Refer to the data table. Polly surveys two more samples. Do the results from these samples support the inference made from the first sample?

• Yes, the survey results support the inference that doing crafts is the least popular hobby at Polly's school.

• No, the survey results does not support the inference that doing crafts is the least popular hobby at Polly's school.

The dot plots show how long it took students in Mr. Chauncey's two science classes to finish their science homework last night. Find the means to make an inference about the data.

• The 1st period mean is 35. The 2nd period mean is 38.75. On average, it took students in the 1st period class slightly longer to finish their homework than it did the students in the 2nd period class.

• The 1st period mean is 38.75. The 2nd period mean is 35. On average, it took students in the 1st period class slightly longer to finish their homework than it did the students in the 2nd period class.

• The 1st period mean is 35. The 2nd period mean is 38.75. On average, it took students in the 2nd period class slightly longer to finish their homework than it did the students in the 1st period class.

• The 1st period mean is 38.75. The 2nd period mean is 35. On average, it took students in the 2nd period class slightly longer to finish their homework than it did the students in the 1st period class.

The dot plot shows a random sample of the number of fish caught and released by 30 participants during a two-day fishing tournament. Select the inference that can be made based on the data collected.

• On average, most participants caught and released 5 or more fish.

• More participants caught 6 fish than any other number.

• The same participants who caught and released 1 fish the first day caught and released 1 fish on the second day.

• On average, participants caught and released more fish on Day 2.

A representative of a car manufacturer in the United States made the following claim in a news report. "Ten years ago, only 53 percent of Americans owned American-made cars, but that figure is significantly higher today." A research group conducted a study to investigate whether the claim was true. The group found that 56 percent of a randomly selected sample of car owners in the United States owned American-made cars. A test of the appropriate hypotheses resulted in a p-value of 0.283. Assuming the conditions for inference were met, is there sufficient evidence to conclude, at the significance level of a = 0.05, that the proportion of all car owners in the United States who own American-made cars has increased from what it was ten years ago?

• Yes, because 0.56 > 0.53.

• Yes, because a reasonable interval for the proportion is 0.56 ± 0.283.

• Yes, because 0.56 - 0.53 = 0.03 and 0.03 < 0.05.

• No, because 0.283 < 0.53.

• No, because 0.283 > 0.05.

A college conducted a survey of randomly selected freshman about their choice of major. The table shows the results of the survey.

What inference about all freshman at this college is best supported by this information?

• The number of freshmen who chose English as their major is less than the number of freshmen who are Undecided on their major.

• The number of freshmen who chose Education as their major is greater than the number of freshmen who chose Science or Other as their major.

• The number of freshmen who chose Business or Education as their major is less than the number of freshmen who chose Science or Engineering as their major.

• The number of freshmen who chose Business as their major is greater than the number of freshmen who chose English as their major.

A local arts council has 200 members. The council president wanted to estimate the percent of its members who have had experience in writing grants. The president randomly selected 30 members and surveyed the selected members on their grant-writing experience. Of the 30 selected members, 12 indicated that they did have the experience. Have the conditions for inference with a one-sample z-interval been met?

• Yes, all conditions for inference have been met.

• No, because the sample size is not large enough to satisfy the conditions for normality.

• No, because the sample was not selected at random.

• No, because the sample size is not less than 10 percent of the population size

• No, because the sample is not representative of the population.

Answer explanation

The sample size of 30 is greater than 10 percent of the population of 200 and risks violating the independence condition.

A state educational agency was concerned that the salaries of public school teachers in one region of the state,region A, were higher than the salaries in another region of the state, region B. The agency took two independent random samples of salaries of public school teachers, one from region A and one from region B. The data are summarized in the table below. Assuming all conditions for inference are met, do the data provide convincing statistical evidence that the salaries of public school teachers in region A are, on average, greater than the salaries of public school teachers in region B?

• Yes, there is evidence at the significance level of a = 0.001.

• Yes, there is evidence at the significance level of a = 0.01 but not at a = 0.001.

• Yes, there is evidence at the significance level of a = 0.05 but not at a = 0.01.

• Yes, there is evidence at the significance level of a = 0.10 but not at a = 0.05.

• No, there is no evidence at the significance level of a = .10.

A group of men and women were surveyed to investigate the association between gender and the number of friends the person has on a social media Web site. Results are shown in the table below. Which of the following procedures is the most appropriate for investigating whether an association exists between gender and the number of friends a person has on a social media Web site?

• A matched-pairs t-test for a mean difference

• A two-sample t-test for the difference between means

• A t-test for the slope of the regression line

• A chi-square goodness-of-fit test

• A chi-square test of independence

The probability that our sample produces a statistic at least as extreme as the one we observed is ________.

• the p-value

• the margin of error

• the critical value

• the test statistic

When we make a generalization about a population based on sample data, we ________.

• conduct an experiment

• perform inference

• interpolate

• extrapolate

• set phasers to stun