The document defines key concepts in hypothesis testing such as critical value, significance level, p-value, type I and type II errors, and power. It states that the critical value divides the normal distribution into regions for rejecting or failing to reject the null hypothesis. The significance level corresponds to the critical region. A p-value less than 0.05 indicates the result is statistically significant. Type I error occurs when the null hypothesis is rejected when it is true, while type II error is failing to reject a false null hypothesis. Power is defined as 1 - β, where β is the probability of a type II error.

1. Critical Value and The P ValueCritical Value and The P Value
Md. Saiful IslamMd. Saiful Islam
Dept. of Pharmaceutical SciencesDept. of Pharmaceutical Sciences
North South UniversityNorth South University
Facebook Group: Pharmacy UniverseFacebook Group: Pharmacy Universe

2. Define Critical Value (or critical region)
The number that divides the normal distribution into region where we will reject the
null hypothesis and the region where we fail to reject the null hypothesis. For
normal distribution Z at 5% level of significance (z= plus-minus 1.96) is often
referred to as the critical value (or critical region).
Define significance level
The value that corresponds to the area in the critical region. When a test statistic
falls in this area, the result is referred to as significant at the alpha level.
What is a Test of significance?
A procedure used to establish the validity of a claim by determining whether or not
the test statistic falls in the critical region. If it does, the results are referred to as
significant.

3. What is P value and how would you interpret it?What is P value and how would you interpret it?
P> 0.05 the result is not significant.P> 0.05 the result is not significant.
P< 0.05 the result is significantP< 0.05 the result is significant
P< 0.01 the result is highly significantP< 0.01 the result is highly significant
P<0.001 the result is very highly significantP<0.001 the result is very highly significant
The lower is the value of P the higher is the likelihood that the test is highlyThe lower is the value of P the higher is the likelihood that the test is highly
statistically significant.statistically significant.
P< 0.05 means the observed difference is too large to be explained by chance alone.P< 0.05 means the observed difference is too large to be explained by chance alone.
The significant level is usually denoted by alpha. It is also magnitude of the errorThe significant level is usually denoted by alpha. It is also magnitude of the error
that one is willing to accept in making the decision to reject the null hypothesis.that one is willing to accept in making the decision to reject the null hypothesis.
Research reports often sate the results are statistically significant ( P < 0.05).Research reports often sate the results are statistically significant ( P < 0.05).

4. Find the value of P if Z= 3.0Find the value of P if Z= 3.0
From normal table this corresponds to 0.0013 for one tail and for two tails 2x0.0013From normal table this corresponds to 0.0013 for one tail and for two tails 2x0.0013
=0.0026. In terms of percentage we can write 0.0013 or .13 percent and for two=0.0026. In terms of percentage we can write 0.0013 or .13 percent and for two
tailed 0.26 percent.tailed 0.26 percent.

5. Define Type one error and Type two errors
Hypothesis typeHypothesis type Ho is trueHo is true Ho is falseHo is false
Accept HoAccept Ho Correct decision (no error)Correct decision (no error) Type II errorType II error
Reject Ho (assume H1 isReject Ho (assume H1 is
true)true)
Type I errorType I error Correct decision ( No error)Correct decision ( No error)
Reject the null hypothesis when it is true is the type one error or error of the
first kind. Type one error is denoted by alpha (α) Accept Ho when it is false
is the type two error or error of the second kind. It is denoted by Beta. (ß)

6. What is power of a test? 1- ß is called the power of a test
Steps in Hypothesis Testing:
Evaluate data
Review assumption
State hypothesis
Select test statistics
Determine distribution of test statistic
State decision rule
Calculate test statistic
Make statistical decision
Do not reject Ho
Reject Ho
Conclude Ho may be true
Calculate Ha is true

7. The different types of statistical tests are
•Normal test or also called z- test
•Students t test
•Paired t test
•Fisher’s t test or two sample means test
•Variance ratio test
•Chi-square test