Preparing to Test a Claim about a Population Proportion Answers

A nutritionist believes that 10% of teenagers eat cereal for breakfast. To investigate this claim, she selects a random sample of 150 teenagers and finds that 25 eat cereal for breakfast. She would like to know if the data provide convincing evidence that the true proportion of teenagers who eat cereal for breakfast differs from 10%. The standardized test statistic is z = 2.72 and the P-value is 0.0066. What conclusion should be made using the = 0.05 significance level?

According to historical data, it is believed that 12% of American adults work more than one job. To investigate if this claim is still accurate, a random sample of 100 American adults is selected. It is discovered that 18 of them work more than one job. A researcher would like to know if the data provide convincing evidence that the true proportion of American adults who work more than one job differs from 12%. What are the values of the test statistic and P-value for this test?Find the z-table here.

It is believed that 80% of adults are honest. An honesty experiment was conducted on a random sample of 50 adults. It was discovered that 42 of the adults were honest. The researcher would like to know if the data provide convincing evidence that more than 80% of adults are honest. The standardized test statistic is z = 0.71 and the P-value is 0.2389. What conclusion should be made using the = 0.10 significance level?

A reporter claims that 90% of American adults cannot name the current vice president of the United States. To investigate this claim, the reporter selects a random sample of 50 American adults and finds that 28 are unable to name the current vice president. The reporter would like to know if the data provide convincing evidence that fewer than 90% of American adults are unable to name the current vice president. Are the conditions for inference met?

According to historical data, it is believed that 12% of American adults work more than one job. To investigate if this claim is still accurate today, a random sample of 100 American adults is selected. It is discovered that 18 of them work more than one job. A researcher would like to know if the data provide convincing evidence that the true proportion of American adults who work more than one job differs from 12%. The standardized test statistic is z = 1.85 and the P-value is 0.0644. What decision should the researcher make using the = 0.05 significance level?

A teacher claims that 55% of her statistics students have a strong understanding of inference for one proportion. To investigate this claim she randomly selects 25 of her 50 statistics students and provides them with an inference problem about one proportion. Of the 25 selected students, 14 demonstrate a strong understanding of inference for one proportion. The teacher would like to know if the data provide convincing evidence that more than 55% of her students have a strong understanding of this topic. Are the conditions for inference met?

According to historical data, it is believed that 12% of American adults work more than one job. To investigate if this claim is still accurate, a random sample of 100 American adults is selected. It is discovered that 18 of them work more than one job. A researcher would like to know if the data provide convincing evidence that the true proportion of American adults who work more than one job differs from 12%. Are the conditions for inference met?

A school administrator claims that 85% of the students at his large school plan to attend college after graduation. The statistics teacher selects a random sample of 50 students from this school and finds that 76% of them plan to attend college after graduation. The administrator would like to know if the data provide convincing evidence that the true proportion of all students from this school who plan to attend college after graduation is less than 85%. The standardized test statistic is z = –1.78 and the P-value is 0.0375. What conclusion should be made using the = 0.01 significance level?

It is claimed that 95% of teenagers who have a cell phone never leave home without it. To investigate this claim, a random sample of 300 teenagers who have a cell phone was selected. It was discovered that 273 of the teenagers in the sample never leave home without their cell phone. One question of interest is whether the data provide convincing evidence that the true proportion of teenagers who never leave home without a cell phone is less than 95%. What are the values of the test statistic and P-value for this test?Find the z-table here.

A teacher attempts to make a number cube unfair by drilling out the spots on one side and inserting lead weights. To determine if she was successful, she rolls the number cube 50 times and keeps track of the number of times she rolls a 1. She rolls a 1 15 times. She would like to know if the data provide convincing evidence that the proportion of rolls that will land on a 1 is greater than one-sixth. Are the conditions for inference met?