Preparing to Test a Claim about a Population Proportion quiz

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?

Because the P-value is greater than = 0.10, there is not convincing evidence that more than 80% of adults are honest.

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?

z = -3.18, P-value = 0.0007

It is claimed that 75% of puppies are house-trained by the time they are 6 months old. To investigate this claim, a random sample of 50 puppies is selected. It is discovered that 42 are house-trained by the time they are 6 months old. A trainer would like to know if the data provide convincing evidence that greater than 75% of puppies are house-trained by the time they are 6 months old. What are the values of the test statistic and P-value for this test?

z = 1.47, P-value = 0.0708

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?

z = 1.85, P-value = 0.0644

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%. What are the values of the test statistic and P-value for this test?

A. one that has pvalue = 0.0066

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. What are the values of the test statistic and P-value for this test?

B.

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?

D. Because the P-value is greater than = 0.01, there is not convincing evidence that the true proportion of all students from this school who plan to attend college after graduation is less than 85%.

It is claimed that 75% of puppies are house-trained by the time they are 6 months old. To investigate this claim, a random sample of 50 puppies is selected. It is discovered that 42 are house-trained by the time they are 6 months old. A trainer would like to know if the data provide convincing evidence that greater than 75% of puppies are house-trained by the time they are 6 months old. The standardized test statistic is z = 1.47 and the P-value is 0.0708. What conclusion should be made using the = 0.05 significance level?

D. Because the P-value is greater than = 0.05, there is not convincing evidence that greater than 75% of puppies are house-trained by the time they are 6 months old.

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?

Fail to reject H0 because the P-value is greater than = 0.05.

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%. The standardized test statistic is z = -3.18 and the P-value is 0.0007. What decision should be made using the = 0.01 significance level?

Reject H0 because the P-value is less than = 0.01.

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?

Yes, the conditions for inference are met.