Inference

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.

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 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 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 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 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

A school administrator is interested in estimating the proportion of students in the district who participate in community service activities. From a random sample of 100 students in the district, the administrator will construct a 99 percent confidence interval for the proportion of all district students who participate in community service activities. Which of the following statements must be true?

• The population proportion will be in the confidence interval.

• The probability that the confidence interval will include the population proportion is 0.99.

• The probability that the confidence interval will include the sample proportion is 0.99.

• The population proportion and the sample proportion will be equal

• The probability that the population proportion and the sample proportion will be equal is 0.99.

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

Which of the following is an appropriate interpretation of a p-value?

• The probability of rejecting H₀, when we should have failed to reject H₀.

• The probability of failing to reject H₀, when we should have rejected H₀.

• Assuming H₀ is true, it is the probability of obtaining our sample statistic or a more extreme value.

• Assuming H₀ is NOT true, it is the probability of obtaining our sample statistic or a more extreme value.