A guide on how to study the two formulas in math and what are their difference.

1. PREPARED BY:

3. - IS A STATISTICAL PROCEDURE USED
TO TEST AN ALTERNATIVE
HYPOTHESIS AGAINST A NULL
HYPOTHESIS.

4. TO DETERMINE WHETHER TWO
SAMPLES’ MEAN ARE DIFFERENT WHEN
VARIANCES/STANDARD DEVIATIONS ARE
KNOWN AND SAMPLE IS LARGE ( n ≥ 30 ).

5. A Z-VALUE( A WHOLE NUMBER/
DECIMAL NUMBER ) WHICH WILL BE
COMPARED TO THE VALUE OF ALPHA(
LEVEL OF SIGNIFICANCE) TO MAKE A
DECISION/ CONCLUSION.

6. FOR THE FORMULA TO BE
USED :
𝜇 is called mu, 𝜎 is called sigma

7. This is the formula for
Standard Deviation:
A population is a collection of persons, objects or items of
interest.
A sample is a portion of the whole and, if properly taken, is
representative of the whole.
The population mean is represented by the Greek
letter mu (μ). It is given by the formula
𝜇 =
𝑥
𝑁
The capital Greek letter sigma (𝚺) is commonly used in
mathematics to represent a summation of all the numbers in
a grouping. N is the number of terms in the population.
The sample mean is represented by x bar . It is given by the
formula
𝑋=
𝑥
𝑛

8. 1.In the population, the average IQ is 100 with
a standard deviation of 15. A team of scientists
wants to test a new medication to see if it has
either a positive or negative effect on
intelligence, or no effect at all.
A sample of 30 participants who have taken
the medication has a mean of 140. Did the
medication affect intelligence, using alpha =
0.05?

9. 𝑋 = 140
𝜇 = 100
𝛿 = 15
n = 30
Ho : 𝜇 = 140
Ha : 𝜇 ≠ 140

10. =
√
140 − 100
15
30
= 14.60
Base on the result of the
computation the z-stat is
14.60. The decision is to
reject the Null Hypothesis
and accept the
Alternative Hypothesis .
Therefore the medication
significantly affected the
intelligence.

11. 2. How do UMD students measure up on the older version of
the verbal GRE? We know that the population average on
the old version of the GRE (from ETS) was 554 with a
standard deviation of 99. Our sample of 90 UMD students
had an average of 568. Is the 14 point difference in
averages enough to say that UMD students perform better
than the general population?
Given in problem: μM = μ = 554, σ = 99
M = 568, N = 90
Remember that if we use distribution of means, we are using
a sample and need to use standard error.
436.10
90
99

N
M



12. Given in problem: μM = μ = 554, σ = 99 M = 568, N = 90
Consult z table for z = 1.34
436.10
90
99

N
M


  34.1
436.10
)554568(





M
MM
z



13. The formula Z-TEST is a
STATISTICAL PROCEDURE used to
test null hypothesis against alternative
hypothesis where the formula is
Where the data needed for the formula
is the mean population( 𝑋), sample
mean(𝜇),standard deviation(𝛿) and the
no.of respondents(n).

14. n
s
x
t 0


15. is a statistical test which is widely used
to compare the mean of two groups of
samples. It is therefore to evaluate
whether the means of the two sets of data
are statistically significantly different from
each other.

16. to be specific, for use with a single
group or sample of data.
when the population
variance is unknown.

17. A T-Value ( A WHOLE NUMBER/ DECIMAL NUMBER )
have to read in t test table the critical value
of t distribution corresponding to the
significance level alpha of your choice
(5%). To make Decision / Conclusion.

18. FOR THE FORMULA TO
BE USED :
a set of values with size n, with
mean 𝑋 and with standard
deviation S. The comparison of
the observed mean 𝑋, of the
population to a theoretical value
μ.

19. A research group claims that
heavy traffic causes
employees to be late by three
days.

20. EMPLOYEE LATE
1 5
2 2
3 4
4 4
5 5
6 3
7 5
8 3
9 4
10 5
11 3
12 5
13 4
14 5
15 2
X-bar = 3.9333
S = 1.1547
n = 15
Ho : LATE = 3 DAYS
Ha : LATE ≠ 3 DAYS

21. n
s
x
t 0

=
3.9333 ─ 3
1.1547
√15
= 3.1303
Base on the result of the
computation the t-stat is
3.1303. The decision is to
reject the Null Hypothesis
and accept the
Alternative Hypothesis .
Therefore the number of
times that the employees
are late is not equal to
three.

22. The formula T-TEST is a
STATISTICAL PROCEDURE
compare the mean of two groups
of samples
Where the data needed for the
formula is the mean population( 𝑋),
sample mean(𝜇),standard
deviation(𝑆) and the no.of
respondents(n).
n
s
x
t 0


23. As to use this formula make sure
that the research is all about the
population and sample mean.
The difference between the two
mean is the basis.
Also by using the formula it will
determine if a certain hypothesis
need to reject or accept.