9.2 Practice

Many new products introduced into the market are targeted toward children. The choice behavior of children with regard to new products is of particular interest to companies that design marketing strategies for these products. As part of one study, randomly selected children in different age groups were compared on their ability to sort new products into the correct product category (milk or juice).12 Here are some of the data.

4 - to 5 -year-olds: n = 50, 10 sorted correctly

6 - to 7 -year-olds: n = 53, 28 sorted correctly

Researchers want to know if a greater proportion of 6- to 7-year-olds than 4- to 5-year-olds can sort correctly. State the appropriate hypotheses for performing a significance test. Be sure to define the parameters of interest.

• H₀: p₁ - p₂ = 0

  H_a:p₁ - p₂ < 0

  where p₁ = the true proportion of 4 to 5 year olds who can sort correctly and p₂ = the true proportion of 6 to 7 year olds who can sort correctly

• H₀: p₁ - p₂ = 0

  H_a:p₁ - p₂ > 0

  where p₁ = the true proportion of 4 to 5 year olds who can sort correctly and p₂ = the true proportion of 6 to 7 year olds who can sort correctly

• H₀: p₁ - p₂ = 0

  H_a:p₁ - p₂ ≠ 0

  where p₁ = the true proportion of 4 to 5 year olds who can sort correctly and p₂ = the true proportion of 6 to 7 year olds who can sort correctly

• H₀: p₁ - p₂ < 0

  H_a: p₁ - p₂ = 0

  where p₁ = the true proportion of 4 to 5 year olds who can sort correctly and p₂ = the true proportion of 6 to 7 year olds who can sort correctly

Many new products introduced into the market are targeted toward children. The choice behavior of children with regard to new products is of particular interest to companies that design marketing strategies for these products. As part of one study, randomly selected children in different age groups were compared on their ability to sort new products into the correct product category (milk or juice).12 Here are some of the data.

4 - to 5 -year-olds: n = 50, 10 sorted correctly

6 - to 7 -year-olds: n = 53, 28 sorted correctly

Researchers want to know if a greater proportion of 6- to 7-year-olds than 4- to 5-year-olds can sort correctly. Check that the conditions for performing the test are met.

• Random? Two separate random samples

  Large Counts? 10, 40, 28, 25 are all ≥ 10

• Random? Two separate random samples

  Large Counts? 10, 40, 28, 25 are all < 10

• Random? Not random samples

  Large Counts? 10, 40, 28, 25 are all ≥ 10

• Fails both

Many new products introduced into the market are targeted toward children. The choice behavior of children with regard to new products is of particular interest to companies that design marketing strategies for these products. As part of one study, randomly selected children in different age groups were compared on their ability to sort new products into the correct product category (milk or juice).12 Here are some of the data.

4 - to 5 -year-olds: n = 50, 10 sorted correctly

6 - to 7 -year-olds: n = 53, 28 sorted correctly

Researchers want to know if a greater proportion of 6- to 7-year-olds than 4- to 5-year-olds can sort correctly.Calculate the standardized test statistic.

• z = -3.45

• z = 3.45

• z = 0.20

• z = 2.79

Many new products introduced into the market are targeted toward children. The choice behavior of children with regard to new products is of particular interest to companies that design marketing strategies for these products. As part of one study, randomly selected children in different age groups were compared on their ability to sort new products into the correct product category (milk or juice).12 Here are some of the data.

4 - to 5 -year-olds: n = 50, 10 sorted correctly

6 - to 7 -year-olds: n = 53, 28 sorted correctly

Researchers want to know if a greater proportion of 6- to 7-year-olds than 4- to 5-year-olds can sort correctly.Calculate the P-value.

• p = 0.0003

• p = 2.7913

• p = 0.3689

• p = 0.0002

Many new products introduced into the market are targeted toward children. The choice behavior of children with regard to new products is of particular interest to companies that design marketing strategies for these products. As part of one study, randomly selected children in different age groups were compared on their ability to sort new products into the correct product category (milk or juice).12 Here are some of the data.

4 - to 5 -year-olds: n = 50, 10 sorted correctly

6 - to 7 -year-olds: n = 53, 28 sorted correctly

Researchers want to know if a greater proportion of 6- to 7-year-olds than 4- to 5-year-olds can sort correctly. What would be the appropriate Conclude part of the 4-step process if you used α = 0.05?

• Because the P-value of 0.003 < α = 0.05, we reject H₀. We have convincing evidence that a greater proportion of 6- to 7-year-olds than 4- to 5-year-olds can sort correctly.

• Because the P-value of 0.003 >α = 0.05, we reject H₀. We have convincing evidence that a greater proportion of 6- to 7-year-olds than 4- to 5-year-olds can sort correctly.

• Because the P-value of 0.003 < α = 0.05, we fail to reject H₀. We don't have convincing evidence that a greater proportion of 6- to 7-year-olds than 4- to 5-year-olds can sort correctly.

• Because the P-value of 0.003 > α = 0.05, we fail to reject H₀. We don't have convincing evidence that a greater proportion of 6- to 7-year-olds than 4- to 5-year-olds can sort correctly.