2. Testing of Hypotheses
A statistical hypothesis is an assumption about a population parameter. This assumption may or
may not be true.
The best way to determine whether a statistical hypothesis is true would be to examine the entire
population. Since that is often impractical, engineers typically examine a random sample from the
population. If sample statistics are not consistent with the statistical hypothesis, the hypothesis is
rejected.
Hypothesis testing
A hypothesis test is a statistical method that uses sample data to evaluate a hypothesis about a
population.
3. Types of Statistical Hypotheses
Null hypothesis
The null hypothesis, assumes that any kind of difference or significance you see in a set
of data is due to chance. The null hypothesis is the initial statistical claim that the
population mean is equivalent to the claimed. The null hypothesis is denoted by Ho.
The opposite of the null hypothesis is known as the alternative hypothesis.
Alternative hypothesis
The alternative hypothesis, denoted by H1or Ha, is the hypothesis that sample
observations are influenced by some non-random cause.
4. Alpha Levels
Usually, we use = 0.05
◦ The alpha level or level of significance is a probability value that is used to
define the very unlikely sample outcomes if the null hypothesis is true.
In this case we would expect to obtain this “outlier” sample in only 5% of the
samples simply by chance.
This corresponds to p = 0.05
In other words, the probability of obtaining this difference by chance is 5%.
5. The critical region is composed of extreme sample values that are very unlikely
to be obtained if the null hypothesis is true.
The boundaries for the critical region are determined by the alpha level. If sample
data fall in the critical region, the null hypothesis is rejected.
Critical Region
6.
7.
8. Test Statistic
A sample statistic or formula which provides a basis for testing the null
hypothesis.
9. State the Null and Alternative
hypotheses
1) Company XYZ manufactures calculators with an average mass of 450g. An engineer believes that average
weight to be different and decides to calculate the average mass of 50 calculators.
2) The teachers in a school believes that at least 80% of students will complete high school. A student disagrees
with this value and decides to conduct a test.
3) A teacher wishes to test if the average GPA of students in the high school is different from 2.7.
4) The percentage of residents who own a vehicle in town XYZ is no more than 75%. A researcher disagrees with
the value and decides to survey 100 residents asking them if they own a vehicle.
10. State the Null and Alternative
hypotheses
1) Company XYZ manufactures calculators with an average mass of 450g. An engineer believes that
average weight to be different and decides to calculate the average mass of 50 calculators.
H0 : = 450 g, H1 : 450 g
2) The teachers in a school believes that at least 80% of students will complete high school. A student
disagrees with this value and decides to conduct a test.
H0 : p 0.80, H1 : p < 0.80
3) A teacher wishes to test if the average GPA of students in the high school is different from 2.7.
H0 : = 2.7, H1 : 2.7
4) The percentage of residents who own a vehicle in town XYZ is no more than 75%. A researcher
disagrees with the value and decides to survey 100 residents asking them if they own a vehicle.
H0 : p 0.80, H1 : p > 0.80
11. Steps for hypothesis testing
1. Formulate H0 :
◦ H0: µ0 = µ or µ0 or µ0
2. Formulate H1 :
◦ H1 : µ1≠ µ0 or µ1 < µ0 or µ1 > µ0
13. Steps for hypothesis testing
4. Choose the distribution and find the variable value or critical value depending on distribution
X (Normal) OR T (t-distribution) OR Y (chi-square)
5. Calculate c the critical point from the respective distribution chart of the distribution
6. Check where the random variable value (X ,T, Y) falls with reference to c, and then according
to the test, fail to reject or reject the hypothesis.
