Question

A research study was performed to determine if more than 30% of first-grade students at one school have entered Piaget’s concrete operational stage of development. A p-value of .021 was computed and the researchers rejected the null hypothesis. They concluded that more than 30% of first-grade students at this school have entered the concrete operational stage of development. However, a census actually found that in the population of all first graders at this school, only 28% have entered the concrete operational stage. Which of the following occurred in this scenario?a) Type I errorb) Type II error

Answer 1

Type I error

Explanation:

A type I error occurs if the null hypothesis is rejected when it is actually true.

Type I Type II

Reject null when true Fail to reject null when not true

Null hypothesis: ∪ = 30%

Alternative hypothesis: ∪ > 30%

The researchers concluded that more than 30% of first-grade students at this school have entered the concrete operational stage of development and they rejected the null hypothesis.

However, a census actually found that in the population of all first graders at this school, only 28% have entered the concrete operational stage.

A type I error has been made because in actuality the null hypothesis was true but was rejected.