Hello I am a B.Sc. statistics and here I lay down few basic examples to understand hypothesis, types of hypothesis, p-value and t-tests.

1. -By Manvendra

2.  Not everything you are told is absolutely certain
 A drug company claims that their miracle drug clears
snoring of 90% of people within 2 weeks, to check this
claim a doctor randomly puts 15 patients to test and the
results were
i. Why did this happen ?
ii. Is the company’s claim false ?
CURED ? YES NO
FREQUENCY 11 4

3.  Hypothesis is a procedure to check possible relationship between 2 or
more variables. Make a judgment about difference between sample
statistic and hypothesized population parameter.
 Population and samples

4. Null/Nil hypothesis (H0)
• Statistical hypothesis
Alternative hypothesis(H1 or Ha)
• Empirical hypothesis

5.  Type I error(α)= When the researcher rejects a null hypothesis
when it is true. The probability of committing a Type I error is called
the significance level.
 Type II error(β)=When the researcher fails to reject a null
hypothesis that is false. The probability of not committing a Type
II error is called the Power of the test.

6. 2-TAIL TEST
Significance level indicate percentage of
sample mean that is outside certain limits.

7. Example, In the United States watch an average of 3 hours of TV per week. To test whether
this claim is true, we record the time (in hours) that a group of 20 American children
(the sample), among all children in the United States (the population), watch TV. The mean
we measure for these 20 children is a sample mean

8. p-value:
The strength of evidence in support of a null hypothesis is
measured by the P-value .The smaller the p-value the more significant is the data.
p-values can only be used to reject the hypothesis and not to consider them. Lies
between 0 and 1.
Example,
A coin is tossed 5 times to check if the coin is unbiased.
Solution:
H0 :The coin is fair v/s H1 :The coin is unfair
The probability of 2 outcomes can be H or T .
The test statistic is 5 by Bernoulli trial,
the p-value is
1
2
^ 5= 0.03125 <0.05
Here p-value<α , Reject H0.
P is low, so the
null must go.

9. For reporting results (e.g. for Minitab),
i. Compute from the observations the observed
value T obs. of the test statistic T (generally at
α=5%)
ii. Calculate the p-value
iii. Decision criterion . If p value<α the decision is to
Reject H0.

10. T-statistic
Properties and
Applications
Interpretation in Minitab

11.  Introduced by William Sealy Gosset
 The basic need of a T-test is to check the null
hypothesis if the means of 2 sample groups are equal. It
is limited to 2 groups
 n<30 and if not it’s assumed to be distributed normally
 The standard deviation of population is unknown

12. • To see if a sample mean is significantly
different from a population mean. Only the
sample s.d. is known.
• Also used for large samples
1 sample
test
• To test if 2 samples representing
different populations have same mean
• Independent of each other
2 sample
test
• 1 sample from which 2 measurements
are made i.e. Dependent
• Used to compare the difference,
BEFORE & AFTER of same
sample
Paired
test

13. 1 sample test 2 sample test Paired test
1)A curious student wants to
check if the human body temp.
is actually 98.6 F
At 5% L.O.S
2) The amount of coffee
(in ounces) filled by a
machine in six randomly
picked jars: 15.7, 15.9, 16.3,
16.2, 15.7 and 15.9. Is the true
mean amount of coffee in a jar
is 16 ounces?
1) To study the effect of drug
with diet alone and diet and
drug considering from 2
different population
2) Below are given the gain in
weights (in lbs) of pigs fed on
two diets A and B
Diet A: 25, 32, 30, 43, 24, 14,
32, 24, 31, 31, 35, 25
Diet B: 44, 34, 22, 10, 47, 31,
40, 30, 32, 35, 18, 21, 35, 29
Test, if the two diets differ
significantly as regards their
effect on increase in weight
1) Mean time taken to sleep
decreases when reading
Hawthorne before sleep. Data
has been obtained for
Hawthorne and without
Hawthorne of same population
within a week’s duration
2) Eleven school boys were
given a test in mathematics.
Do the marks give evidence
that the student’s have
benefited by the extra
coaching? Marks in test-1: 23,
20, 19, 21, 18, 20, 18, 17, 23,
16, 19
Marks in test-2: 24, 19, 22, 18,
20, 22, 20, 20, 23, 20

14. USING
MINITAB