Question

Children make choices 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). Here are some of the data:

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

a. State appropriate hypotheses for performing a significance test. Be sure to define the parameters of interest.

b. Check if the conditions for performing the test are met.

Short answer

a. The hypothesis is $H_0:p_1=p_2$and $H_a:p_1<p_2$

b. All conditions are met.

Step-by-step solution

Given Information

Researchers want to know if a greater population of $6-7$years old can sort correctly than $4-5$years old or not.

$x_1=10$

$x_2=28$

$n_1=50$

$n_2=53$

Appropriate hypothesis for performing significance test

Claim: Proportion is greater for $6-7$years old.

Finding hypothesis:

As per the given data, hypothesis are:

$H_0:p_1=p_2$

$H_a:p_1<p_2$

$p_1$is proportion of $4-5$years old who can sort correctly.

$p_2$is proportion of$6-7$years old who can sort correctly.

Checkimg conditions

The conditions are:

Random: Children are independent random sample.

Independent: $50<10\%$of all $4-5$old and $53<10\%$of all $6-7$years old.

Normal: There are $10$success and $40$failures in first sample and $28$success and $25$failures which are greater than ten.

All conditions are satisfied. It is appropriate to use hypothesis test.