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 180 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 different 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.

a) The symbol for the random variable involved in this problem is ______

The wording for the random variable in context is as follows: _________

b) The symbol for the parameter involved in this problem is __________

The wording for the parameter in context is as follows: ________

c) Fill in the correct null and alternative hypotheses:

H0:_______

HA:_______

d) A Type I error in the context of this problem would be:

e) A Type II error in the context of this problem would be:

  

Answer 1

Answer: 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 180 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 different percentage of left-handers than the general American population?

Solution:

a) The symbol for the random variable involved in this problem is :

The symbol for the random variable is .

The wording for the random variable in context is as follows:

In random sample of 180 the percentage of all students from that college that are left-handed.

b) The symbol for the parameter involved in this problem is:

the symbol for the parameter is p

The wording for the parameter in context is as follows:

11% of all students from that college are left-handed.

c) Fill in the correct null and alternative hypotheses:

Null hypothesis, Ho: p = 0.11

Alternative hypothesis, Ha: p > 0.11

d) A Type I error in the context of this problem would be:

Type I error is rejecting Ho, when Ho is true

Rejecting that the percentage of all students from the college that are left-handed is 11% when the percentage is really 11%.

e) A Type II error in the context of this problem would be:

Type II error is fail to reject Ho, when Ho is false

Failing to reject that the percentage of all students from the college that are left-handed is 11% when the percentage is really higher than that.