Lesson 6 Normal Distribution

Question 1

is represented by the well known bell-shaped

Answer 1

Normal distribution

Question 2

is a distribution with population mean = 0 and standard deviation = 1.

Answer 2

Standard normal distribution

Question 3

Essential Properties of the Normal Distribution

Answer 3

1. Mean = Median = Mode
2. It is symmetrical about the mean.
3. The tails or ends are asymptotic relative
   to the horizontal.
4. Approximately 68% of the normal population
   lies within 1 standard deviation of the mean
5. Approximately 95 of the normal distribution lies within 2 standard deviation of the mean.
6. The total area under the normal distribution curve is 1, or 100%.
7. The normal distribution curve area may be subdivided into standard deviations, at least 3 units to the left and 3 units to the right of the vertical line.
8. The probability that a randomly selected x of a normal population lies between two values XL and XR

Question 4

z score formula

Answer 4

z = (x - μ) / σ

where: z = z value
x = the value of any particular observation or measurement
μ = the mean of the distribution
σ = standard deviation of the distribution

Question 5

a normal distribution can be converted into standard normal distribution by obtaining the

Answer 5

z value

Question 6

is the sign distance between a selected value, designated х, and the mean, μ, divided by the standard deviation

Answer 6

z value

Question 7

Process of making an inference or a generalization on a population based on the results of the study on samples

Answer 7

Hypothesis testing

Question 8

is a guess or prediction made by a researcher regarding the possible outcome of the study.

Answer 8

Statistical hypothesis testing

Question 9

Two (2) types of statistical hypothesis

Answer 9

Null hypothesis (Ho)
Alternative hypothesis (Ha)

Question 10

• It is the hypothesis to be tested which one hopes to reject.
• It shows equality or no significant difference or relationship between variables
• That NO statistically significant difference exists between the population parameter and the sample statistic being compared

Answer 10

Null hypothesis (Ho)

Question 11

• It generally represents the idea which the researcher wants to prove
• Logical opposite of the null hypothesis
• That a statistically significant difference DOES EXIST between the population parameter and the sample statistic being compared

Answer 11

Alternative hypothesis (Ha)

Question 12

Types of hypothesis testing

Answer 12

One-Tailed
Two-Tailed

Question 13

It is a directional test with the region of rejection lying either left or right on the alternative hypothesis.

Answer 13

One-Tailed Test

Question 14

The region of rejection is on the right tail

Answer 14

Right directional test

Question 15

It is used when Ha uses comparatives such as
greater than,
higher than,
better than,
superior to,
exceeds, etc.

Answer 15

Right directional test

Question 16

The region of rejection is on the left tail.

Answer 16

Left directional test

Question 17

It is used when Ha uses comparatives such as
less than,
smaller than,
inferior to,
lower than,
below, etc.

Answer 17

Left directional test

Question 18

It is a non-directional test with the region of rejection lying on both tails of the normal curve.

Answer 18

Two-Tailed Test

Question 19

It is used when Ha uses word such as
Not equal to,
Significantly different, etc.

Answer 19

Two-Tailed Test

Question 20

The error committed when the null hypothesis is rejected when in fact ** it is true** and the alternative hypothesis is false.

Answer 20

Type I error

Question 21

The error committed when the **null hypothesis is accepted ** when in fact it is false and the alternative hypothesis is true.

Answer 21

Type II error

Question 22

The probability of committing a Type I error is designated by

Answer 22

alpha (α)

Question 23

the probability of committing a Type II error is designated by

Answer 23

beta (β).

Question 24

the size of the rejection region

Answer 24

Alpha (α)

Question 25

the size of the acceptance region.

Answer 25

Beta (β)

Question 26

The most popular level of significance of alpha (α) are

Answer 26

0.01 and 0.05 levels

Question 27

5 steps in testing the hypothesis

Answer 27

1. Formulate Ho and Ha.
2. Set the level of significance α, then determine the type of hypothesis test and the tabular or p-value.
3. Set the criterion (when to reject Ho), determine and compute for the test statistic.
4. Make your decision.
5. Formulate your conclusion

Question 28

Testing the hyphothesis

A. Using tabular value of Z.

Answer 28

1. One-tailed test (right directional)
   “Reject Ho if Z computed is greater than or equal to Z tabular.”
2. One-tailed test (left directional)
   “Reject Ho if Z computed is less than or equal to Z tabular”
3. Two-tailed test (Z computed is positive)
   “Reject Ho if Z computed is greater than or equal to Z tabular.”
4. Two-tailed test (Z computed is negative)
   “Reject Ho if Z computed is less than or equal to Z tabular”

Question 29

Testing the hyphothesis

B. Using the p-value

Answer 29

Reject Ho if the probability is less than or equal to alpha (α).

Question 30

used when n is large, n ≥ 30

Answer 30

The Z-test

z = (x̄ - μ) √n / σ

Where:
σ is the population standard deviation
X is the sample mean
µ is the population mean
n is the sample size