AP Stat Unit 6 Progress Check: MCQ Part B

A study reports that 75 percent of young adults in a county get their news from online sources. A sociologist believes that the percentage is actually greater than 75 percent. The sociologist will select a random sample of young adults from around the county to interview. Which of the following is the most appropriate method for investigating the sociologist's belief? - Answer- A one-sample z-test for a population proportion A study reported that 28 percent of middle school students in a certain state participate in community service activities. A teacher believes that the rate is greater than 28 percent for the middle school students in the teacher's district. The teacher selected a random sample of middle school students from the district, and the percent of students in the sample who participated in community service activities was found to be 32 percent. Which of the following is the most appropriate method for investigating the teacher's belief? - Answer- A one-sample z-test for a population proportion A workers' representative for a large factory believes that more than half the workers at the factory want the opportunity to work more overtime hours. Which of the following are the appropriate hypotheses to test the representative's belief? - Answer- H0:p=0.5 Ha:p>0.5 A manufacturer of cell phone screens is concerned because 12 percent of the screens manufactured using a previous process were rejected at the final inspection and could not be sold. A new process is introduced that is intended to reduce the proportion of rejected screens. After the process has been in place for several months a random sample of 100 screens is selected and inspected. Of the 100 screens 6 are rejected. What are the appropriate hypotheses to investigate whether the new process reduces the population proportion of screens that will be rejected? - Answer- H0:p=0.12 Ha:p<0.12 A one-sample z-test for a population proportion p will be conducted. Which of the following conditions checks that the sampling distribution of the sample proportion is approximately normal? I. The sample is selected at random. II. np0≥10 and n(1−p0)≥10 for sample size n. III. The sample size is less than or equal to 10 percent of the population size. - Answer- II only A newspaper article claims that 92 percent of teens use social media. To investigate the claim, a polling organization selected a random sample of 100 teens, and 96 teens in the sample indicated that they use social media. Given the data, why is it not appropriate to use a one-sample z-test for a proportion to test the newspaper's claim? - Answer- The expected number of teens in the sample who do not use social media is less than 10.