9.2 Day 2 Check Your Understanding

Sometimes parents and grandparents like to recount how difficult life was when they were kids, such as having to walk 10+ miles to school (in the snow, uphill both ways). A random sample of 180 teenagers were selected and 40% had heard stories from their parents or grandparents about how difficult life was when they were kids. Do these data provide convincing evidence at the α = 0.05 significance level that the proportion of all teenagers who have heard stories from their parents or grandparents about how difficult life was when they were kids differs from 0.50?

Identify the "State" portion of the significance test.

• Ho: p = 0.50

  Ha: p > 0.50

  p = the true proportion of all teens who have heard stories at the α = 0.05

• Ho: p = 0.50

  Ha: p does not equal 0.50

  p = the true proportion of all teens who have heard stories α = 0.05

• Ho: p = 0.50

  Ha: p < 0.50

  p = the true proportion of all teens who have heard stories at the α = 0.05

Sometimes parents and grandparents like to recount how difficult life was when they were kids, such as having to walk 10+ miles to school (in the snow, uphill both ways). A random sample of 180 teenagers were selected and 40% had heard stories from their parents or grandparents about how difficult life was when they were kids. Do these data provide convincing evidence at the α = 0.05 significance level that the proportion of all teenagers who have heard stories from their parents or grandparents about how difficult life was when they were kids differs from 0.50?

What would be the "Plan" proportion of the significance test?

Sometimes parents and grandparents like to recount how difficult life was when they were kids, such as having to walk 10+ miles to school (in the snow, uphill both ways). A random sample of 180 teenagers were selected and 40% had heard stories from their parents or grandparents about how difficult life was when they were kids. Do these data provide convincing evidence at the α = 0.05 significance level that the proportion of all teenagers who have heard stories from their parents or grandparents about how difficult life was when they were kids differs from 0.50?

What is the test statistic?

• 0.40

• -2.74

• 0.50

• -2.68

Sometimes parents and grandparents like to recount how difficult life was when they were kids, such as having to walk 10+ miles to school (in the snow, uphill both ways). A random sample of 180 teenagers were selected and 40% had heard stories from their parents or grandparents about how difficult life was when they were kids. Do these data provide convincing evidence at the α = 0.05 significance level that the proportion of all teenagers who have heard stories from their parents or grandparents about how difficult life was when they were kids differs from 0.50?

What is the p-value?

• 0.0072

• 0.0036

• 0.0031

• 0.0061

Sometimes parents and grandparents like to recount how difficult life was when they were kids, such as having to walk 10+ miles to school (in the snow, uphill both ways). A random sample of 180 teenagers were selected and 40% had heard stories from their parents or grandparents about how difficult life was when they were kids. Do these data provide convincing evidence at the α = 0.05 significance level that the proportion of all teenagers who have heard stories from their parents or grandparents about how difficult life was when they were kids differs from 0.50?

Which is the correct conclusion to the significance test?

• Because 0.0061 < 0.05 we fail to reject Ho. We do not have convincing evidence that the true proportion of teenagers who have heard stores differs from 0.50.

• Because 0.0061 < 0.05 we reject Ho. We do have convincing evidence that the true proportion of teenagers who have heard stores differs from 0.50.

• Because 0.0072 < 0.05 we fail to reject Ho. We do not have convincing evidence that the true proportion of teenagers who have heard stores differs from 0.50.

• Because 0.0072 < 0.05 we reject Ho. We do have convincing evidence that the true proportion of teenagers who have heard stores differs from 0.50.

A 95% confidence interval for the proportion of all teenagers who have heard stories from their parents or grandparents about how difficult life was when they were kids is (0.328, 0.472). Explain how the confidence interval is consistent with, but gives more information than, the test.