Question

It is believed that 11% of all Americans are left-handed. A college needs to know the number of left-handed desks to place in the large instructional lecture halls being constructed on its campus. In a random sample of 140 students from that college, whether or not a student was left-handed is recorded for each student. The college wants to know if the data provide enough evidence to show that students at this college have a lower percentage of left-handers than the general American population. State the random variable, population parameter, and hypotheses. State the Type I and Type II errors in the context of this problem.

Answer 1

a) State the random variable

Random variable : x

which refers to a randomly selected student from the college that is left-handed.

b) state population parameter

population parameter : P

which is the percentage of all students from the college that are left handed

c) state the hypotheses

The hypothesis are;

Null hypothesis H₀ : p = 0.11

Alternative hypothesis H₁ : p > 0.11

d) State the Type I error in the context of this problem.

Type - I Error: Rejecting that the % of all the students from the college that are left-handed is 11% when actually the % is really 11%

(Reject H₀ when H₀ is true)

e) State the Type 11 error in the context of this problem

Type-II Error: Failing to Reject that the % of all the students from the college that are left-handed is 11% when the % is really higher than that

(Fail to reject H₀ when H₀ is false)