Question

It is believed that 11% of all Americans are left-handed. A college needs to know how many left-handed desks to place in the big lecture halls being constructed on its campus. In a random sample of 120 students from that college, whether or not a student was left-handed was recorded for each student. The college wants to know if the data provide enough evidence to show that students at this college have a higher percentage of left-handers than the general American population?

Required:
a. State the random variable, population parameter, and hypotheses.
b. State the Type I and Type II errors in the context of this problem.

Answer 1

(a) H₀: p = 0.11 vs. Hₐ: p > 0.11.

(b) A type I error occurs when we discard a true null hypothesis (H₀) and a type II error is made when we fail to discard a false null hypothesis (H₀).

Explanation:

A college needs to know how many left-handed desks to place in the big lecture halls being constructed on its campus.

From past data, it is believed that 11% of all Americans are left-handed.

The college wants to know if the data provide enough evidence to show that students at this college have a higher percentage of left-handed people than the general American population.

(a)

The hypothesis can be defined as follows:

H₀: The percentage of left-handed people in the college is 11%, i.e. p = 0.11.

Hₐ: The percentage of left-handed people in the college is more than 11%, i.e. p > 0.11.

(b)

A type I error occurs when we discard a true null hypothesis (H₀) and a type II error is made when we fail to discard a false null hypothesis (H₀).

In this case, a type I error would be committed if it is concluded that the percentage of left-handed people in the college is more than 11% when in fact it is 11%.

And, a type II error would be committed if it is concluded that the percentage of left-handed people in the college is 11% when in fact it is more than 11%.