Normal Distribution and Statistical Hypothesis Testing

Question 1

is a distribution that is symmetric about the mean, continuous variables

Answer 1

Normal Distribution/ Probability Distribution Curve

Question 2

mean, median, mode are approximately same

Probability distribution curve

Answer 2

Normal (no skewed)/ Gaussian Curve
(Graphical distribution of probability
Data is spread normally)

Question 3

mean, median, mode are not same

Many outlier that are lower than mean

Answer 3

Negatively skewed
(Mean < median < mode (mean and median is greater than the mean)
Left tail is dragging mean)

Question 4

Many outliers that are higher than the mean

Mode < median < mean

Answer 4

Positively skewed
Data set that has extreme values larger than the mean
Right tail is dragging mean

Question 5

distortion
Asymmetry that deviates from the symmetrical bell-curve/ normal distribution
Imbalance in the distribution of data relative to the mean

Answer 5

Skewness

Values plotted will be -3 to +3

Question 6

extreme observations/ values, far from the values observed

Answer 6

Outliers

Question 7

measures the peak or flatness of data set

Answer 7

Kurtosis

Question 8

negative kurtosis, flat/ low peak, short tail

Answer 8

Platykurtic

Question 9

normal distribution (kurtosis)

Answer 9

Mesokurtic

Question 10

Characteristics of a Normal Distribution:
follows a consistent pattern
Earliest distribution to be well studied
First equation is derived by Abraham de Moivre

Answer 10

Bell shaped and symmetric about the mean
(Friedrich Gauss: work became well known
Symmetrical and mesokurtic)

Question 11

Characteristics of a Normal Distribution:
Mean = median = mode
____: center of the curve
____: only 1, peak of curve

Answer 11

Mean

Mode

Question 12

Characteristics of a Normal Distribution:

Total area under the curve (AUC) is ____%

Answer 12

1 or 100

Question 13

Characteristics of a Normal Distribution:
Has long tapering tails that extend infinitely in either direction but never touching the x-axis
____: lines that as it gets closer but never reach/ touch the x-axis

Answer 13

Asymptote

Question 14

Characteristics of a Normal Distribution:
Completely determined by two parameters, its ___ (μ) and __ (𝜎, sigma)
____: location of the curve in x-axis
____: spread of curve

Answer 14

Mean
SD
(𝜎 increases, distribution becomes wider; low peak
𝜎 decreases, distribution becomes thinner; high peak)

Question 15

1 SD covers __% of the distribution
2 SD covers __% of the distribution
3 SD covers __% of the distribution

Answer 15

68
95
99.7

Question 16

Importance of Normal Distribution:
Useful for explaining many ______ _______
Even if the distribution of the variable is not normal, can easily transform using log, square root or other transformation to make it approximate the normal distribution
Most measurements/ variables are normally distributed

Answer 16

biological phenomena

Question 17

Importance of Normal Distribution:
Plays an important role in ______ ______because:
Many statistical test assume normality of the distribution
The other important distributions (binomial, t-distribution) can be approximated by the normal esp. when the sample size is large enough
The sampling distribution of the mean is approximately normal if the sample size is large enough (central limit theorem)

Answer 17

statistical inference

Question 18

Mean =0, SD =1
Capital ‘Z’ is traditionally used to represent the standard normal random variable
Small letter ‘z’ is used to represent a particular value of Z

Answer 18

The Standard Normal Distribution
Areas under the standard normal are tabulated
Any value x from the normal distribution can be transformed into a standard normal value of z using the formula

Question 19

Statement about the value of a population parameter

Mean, median, mode, variance, SD, proportion, total

Answer 19

Statistical Hypothesis

Question 20

Assertion or proposition about the relationship between 2 or more variables
Concerned w/ the parameters of population

Answer 20

Statistical Hypothesis

Formulated as a result of years of observation and research

Question 21

Method of making decision using data, whether from a controlled experiment or an observational study (not controlled)

Answer 21

Statistical Hypothesis

Question 22

Set of procedures that culminates in either rejection or non-rejection of null hypothesis
Involves the comparison of two hypotheses: Null and Alternative

Answer 22

Statistical Hypothesis

Hypothesis: prediction, educated guess of the results, should be testable

Question 23

p< alpha: probability of occurrence of sample results is low, _____ null hypothesis
p> alpha: probability of occurrence of sample results is high, _____ null hypothesis

Answer 23

reject

not reject

Question 24

7 Steps of Hypothesis Testing

SSSDCMD

Answer 24

State the null (H0) & alternative (H1 or H0) hypothesis
State the Level of Significance
Select the appropriate test statistic/ test criterion
Determine the Critical Region or Region of Rejection
Compute the test-statistic
Make a Statistical Decision
Draw conclusion

Question 25

(H0): Statement of equality | Hypothesis of no difference

Answer 25

Null hypothesis | Often used to signify zero treatment effect or the equivalence of population parameters or to a specified value

Question 26

Usually the research hypothesis (the hypothesis the investigator believes in) What you believe to be true in population

Answer 26

Alternative hypothesis (Ha) (Uses or ≠ sign If P is low, then the null (H0) must go)

Question 27

Ho vs Ha: The proportion of students who obtain a grade of 2.0 or better among those using models for demonstration, PM, is equal to the proportion among those using cadavers, PC

Answer 27

Ho: PM = PC (”no difference”, equal)

Question 28

Ho vs Ha: The proportion of students who obtain a grade of 2.0 or better among those using models for demonstration, PM , is not equal to the proportion among those using cadavers, PC

Answer 28

Ha: PM ≠ PC (”two-tailed test”, not equal)

Question 29

Ho vs Ha: The proportion of students who obtain a grade of 2.0 or better among those using models for demonstration, PM , is greater than to the proportion among those using cadavers, PC

Answer 29

HA: PM > PC (”one-tailed test”, greater or less than; can also use

Question 30

Types of Ha: Simply states that there is difference in the groups being compared But did not indicate w/c one is greater or less than

Answer 30

Non-directional (two-tailed test, not equal):

Question 31

Types of Ha: Specifies direction if disagreement with H0 Has a direction, says which one is longer or shorter

Answer 31

Directional (one-tailed test)

Question 32

(𝛂); alpha (set before data collection, low value) | Is set arbitrarily by research before collecting data

Answer 32

Level of significance | Usually set as 0.05, 0.1 or 0.01

Question 33

Types of Error: Error of rejecting a true null hypothesis Alpha is kept at a low level when it is important not to make a mistake of rejecting a true H0 Higher alpha, lower beta

Answer 33

Type I error (𝛼)

Question 34

Types of Error: Error of not rejecting a false null hypothesis Beta is kept at a low level when it is important not to accept a false H0 Probability of not rejecting a false null hypothesis Inversely related to alpha: lower alpha, higher beta

Answer 34

Type II error (𝜷)

Question 35

Found at the tail end of distribution Set of value of test statistics which leads to the rejection of the null hypothesis Value of test statistics that corresponds to alpha (level of significance)

Answer 35

Area of Rejection

Question 36

Basic formula of the test statistic: numerical data from the sample:

Answer 36

Formula: test statistic = observed statistic - expected parameter under H0/ standard error

Question 37

always towards the null hypothesis | Whether to reject or not reject the null hypothesis

Answer 37

Statistical decisions

Question 38

Ways for Making Statistical Decision: Compare _____ with the_____ Where did the test statistic fall: critical or non-rejection region

Answer 38

test statistic , critical region

Question 39

Ways for Making Statistical Decision: Compare _____ with the_____ Statistical software automatically give this value

Answer 39

p-value , a(level of significance)

Question 40

Rejection or Non-rejection of Ho: “There is sufficient evidence to say that (alternative hypothesis)” Ex: There is sufficient evidence to say that the proportion of students who obtain a grade of 2.0 or better among those using models for demonstration, PM, is not equal to the proportion among those using cadavers, PC

Answer 40

Rejection of the Null Hypothesis (H0)

Question 41

Rejection or Non-rejection of Ho: “There is no sufficient evidence to say that (alternative hypothesis)” Ex: There is no sufficient evidence to say that the proportion of students who obtain a grade of 2.0 or better among those using models for demonstration, PM, is not equal to the proportion among those using cadavers, PC

Answer 41

Non-rejection of the Null Hypothesis (H0) leads to a conclusion stated this way

Question 42

Reject or Do not reject or Non-rejection: (Ho) Sample does not come from a population with the same parameter values defined by null hypothesis Sample value cannot support/ not consistent with the null hypothesis

Answer 42

Reject H0

Question 43

Reject or Do not reject or Non-rejection: (Ho) Conclude that there is no sufficient evidence to say that Ha is NOT true H0 is not accepted

Answer 43

Do not reject H0

Question 44

Reject or Do not reject or Non-rejection: (Ho) | Not proof that the null hypothesis is correct

Answer 44

Non-rejection H0

Question 45

Factors that result to non-rejection: Insufficient ____ to conclude Ha rather than proof of H0 Inadequate ____ ____ problems

Answer 45

proof sample size measurement