fail to reject the null hypothesis.
However, errors could be made in some decisions, which we can divide in two.
1.
A
type I error
occurs if the null hypothesis is rejected when it is true.
2.
A
type II error
occurs if the null hypothesis is not rejected when it is false.
Note
: No matter which hypothesis represents the claim, always begin the hypothesis test
assuming that
the null hypothesis is true
.
Example 4
FEU Institute of Education claims that 89% of their graduates find employment within six months of
graduation.
What will a type I or type II error be?
•
A type I error is rejecting the null when it is true.
The population proportion is actually 0.89, but is rejected.
(We believe it is not 0.89.)
•
A type II error is failing to reject the null when it is false.
The population proportion is not 0.89, but is not rejected.
(We believe it is 0.89.)
2.
A laptop manufacturer claims that the mean life of the battery for a certain model of laptop
is more than 5 hours.
3.
An amusement park claims that the mean daily attendance at the park is at least 17,450
people.
4.
The standard deviation of the base price of a certain type of all-terrain vehicle is no more
than Php 28,300.
Learning Activity 2
In reference to Learning Activity 1, construct a sentence of what could be a type I and type II error
for each of the given scenario.

Science, Technology, Engineering and Mathematics
Statistics and Probability
SY 2020
–
2021
Page
4
of
11
Lesson 13.3
–
Level of Significance
In a hypothesis test, the
level of significance
is your maximum allowable probability of making a type I
error.
It is denoted by
, the
lowercase Greek letter alpha
. By setting the level of significance at a small
value, you are saying that you want the probability of rejecting a true null hypothesis to be small.
Commonly used levels of significance:
•
= 0.10
•
= 0.05
•
= 0.01
Meanwhile, the probability of making a type II error is denoted by
1 -
,
where
is the
lowercase Greek
letter beta
.
Lesson 13.4
–
Statistical Tests
After stating the null and alternative hypotheses and specifying the level of significance, a random sample
is taken from the population and sample statistics are calculated. The statistic that is compared with the
parameter in the null hypothesis is called the
test statistic
.
Population
parameter
Test statistic
Standardized
test statistic
μ
(mean)
𝑥̅
z (n
30)
t (n < 30)
p (proportion)
ˆ
p
z
2
(variance)
s
2
X
2
(chi-square)
Lesson 13.5
–
P-Value
Another way of expressing the level of statistical significance is using P-values, which is based on the
normal distribution. A
P-value
(or
probability value
) of a hypothesis test is the probability of obtaining
a sample statistic with a value as extreme or more extreme than the one determined from the sample data.
The smaller the p-value, the stronger the evidence that you should reject the null hypothesis.