Z-test in Statistics, hypotheses

1. Good Morning!

Prepared by:
Aljon A. Casupanan
(BSEd III – Compassion)

3. Today’s Lesson:
Z Test
(Two Sample Mean
Test)

4. Z Test (Two Sample Mean Test)
Z test can be used in:
• Education
• Business
• Engineering

5. We need to:
• Accept Ho and Reject Ha when:
the p value is greater than the level of
significance.
(p value > 휶)
• Accept Ha and Reject Ho when:
the p value is less than the level of significance.
(p value < 휶)

6. When do we use Z Test (Two
Sample Mean)?
When two separate samples are drawn
at random.
When testing whether the two
samples are taken from a single
population.

7. When do we use Z Test (Two
Sample Mean)?
It is necessary that the sample must
be independent.

8. Steps In Hypothesis Testing (Z
Test Two Sample Mean Test)
Step 1:State the null and alternative
hypotheses
Step 2: Identify or select the level of
significance and the p - value
Step 3: Compute the test statistic
Step 4: Decision,whether to accept the null
hypothesis (Ho) and reject alternative
hypothesis (Ha) or vice versa
Step 5: State the conclusion.

9. Formula in Computing the Test Statistic
Using Z Test (Two Sample Mean Test)
• when the given means
are sample means.
풛 =
풙₁ − 풙₂
풔₁²
+
풏₁
풔₂²
풏₂
• when the given means
are population means.
풛 =
흁₁ − 흁₂
흈₁²
+
풏₁
흈₂²
풏₂
풙₁ = mean of the 1st sample
풙₂ = mean of the 2nd sample
흁₁ = mean of the 1st population
흁₂ = mean of the 2nd population
퐬₁ = standard deviation of the 1st
sample
퐬₂ = standard deviation of the 2nd
sample
흈₁ = standard deviation of the 1st
population
흈₂ = standard deviation of the 2nd
population
풏₁ = size of the 1st sample or
population
풏₂ = size of the 2nd sample or
population

10. We need to:
• Accept Ho and Reject Ha when:
the p value is greater than the level of
significance.
(p value > 휶)
• Accept Ha and Reject Ho when:
the p value is less than the level of significance.
(p value < 휶)

11. Problem 1:
Example 1. A bank is opening
a branch in one of two
neighborhoods. One of these
factors considered by the
bank was whether the
average monthly family
income (in thousand pesos )
in the two neighborhoods
differed. From census
records, the bank drew two
random samples of 100
families and obtained the
following information:
Sample A Sample B
퐱 ₁ = ퟏퟎ, ퟏퟎퟎ 퐱 ₂ = ퟏퟎ, ퟑퟎퟎ
s₁ = 300 s₂ = 400
n₁ = 100 n₂ = 100
The bank wishes to test the null
hypothesis that the two
neighborhoods have the same
mean income. What should the
bank conclude using 휶 = ퟎ. ퟎퟓ?

12. Problem 2:
• An examination is given to 2 classes containing
40 and 50 students respectively. In the first
class, the mean grade was 74 with a standard
deviation of 8, while in the second class the
mean grade was 78 with a standard deviation
of 7. Is there a significant difference between
the performance of the 2 classes at 0.05
significance level?

13. QUIZ #2

14. Answer the following: (Show your step by step
solutions in numbers 1 and 2)
1. .The mean height of 50 male students who
showed above average participation in college
athletics was 68.2 inches with a standard
deviation of 2.5 inches while 50 male students
who showed no interest in such participation had
mean height of 67.5 inches and a standard
deviation of 2.8 inches. Test the hypothesis that
male students who participated in college
athletics are taller than other male students at
0.05 level of significance. (15 points)

15. • 2. The IQs of 16 students from one
area of the city showed a mean of
107 with a standard deviation of 10,
while the IQs of 14 students from
another area of the city showed a
mean of 112 with a standard
deviation of 8.Is there a significant
difference between the IQs of the
two groups?Use 0.01 level of
significance. (15 points)

16. 3. How does z test (one sample mean)
differ from z test (two samplemean)?
(3 points)
4. How can we apply or use z test (two
sample mean) in our real lives? (2 points)