Read Discuss Courses Practice We will be trying to understand the T-Test in R Programming with the help of an example. Suppose a businessman with two sweet shops in a town wants to check if the average number of sweets sold in a day in both stores is the same or not. So, the businessman takes the average number of sweets sold to 15 random people in the respective shops. He found out that the first shop sold 30 sweets on average whereas the second shop sold 40. So, from the owner’s point of view, the second shop was doing better business than the former. But the thing to notic

2. Confidence Limits:
Confidence Limit is range within which all the Possible
sample mean will lie.
 A population mean ± 1 Std. Error limitcorrespond to
68.27 percentof sample meanvalue.
 A population mean ± 1.96 Std. Errorcorrespond to
95.0% of thesample mean values.
 Population mean ± 2.58 stand. Errorcorresponds to 99
% sample meanvalues.
 Population mean ± 3.29 correspond to 99.9% of the
sample meanvalue.
• Interval is confidence interval.

3. • A confidence interval, in statistics, refers to the
probability that a population parameter will fall
between a set of values for a certain proportion of
times.
• Analysts often use confidence intervals that
contain either 95% or 99% of expected
observations.
• Thus, if a point estimate is generated from a
statistical model of 10.00 with a 95% confidence
interval of 9.50 - 10.50, it can be inferred that
there is a 95% probability that the true value falls
within that range.

7. • Hypothesis:
A statistical Hypothesis is a statement about the parameter
(formsof population).
i.e. x1 = x2 or x = µ or p1 = p2 orp = P
• Null Hypothesis (H0):
It is hypothesis of no difference between two outcome
variables.
• Alternative Hypothesis (H1):
There is difference between the twovariables understudy.
• Hypotheses are always about parameters of populations,
never about statistic from samples.
• Testof Significance:
Testing the null hypothesis.

8. Steps of hypothesis testing
• Defining the research question.
• Null Hypothesis (H0) - there is no difference between the
group.
• Alternative hypothesis (H1) – there is some difference
between thegroups.
• Selecting appropriate test.
• Calculationof testcriteria (c).
• Deciding the acceptable level of significance (α). Usually
0.05 (5%).
• Compare the test criteriawith theoretical valueat α.
• Accepting Null Hypothesisor Alternative Hypothesis.
• Inference.

10. One Sided ( One tailed) Vs. Two Sided (two
tailed) :
• Two Sided test:
Significantly large departure from Null Hypothesis in
eitherdirection will be judged by significance.
• One Sided Test:
Is used we are interested in measuring thedeparture in
only one particulardirection.
• A one sided test at level P is sameas two sided test at level
2P.
• Example: test tocompare population mean of twogroup A
and B
– Alternate Hypothesis mean of A > mean of B. – One tailed test.
– Alternate Hypothesis Mean of B > mean of A > meanof B. – two
tailed test.

11. Type -1 Error
 Rejecting a null hypothesis (H0) when
it is true that is called type-1 error
Type-2 Error
 Accepting a null hypothesis (H0)
when it is false that is called type-2 error

14.  The power of a test is the probability
of rejecting the null hypothesis when it is
false
 It is the probability of avoiding a type
II error.
 The power may also be thought of as
the likelihood that a particular study will
detect a deviation from the null
hypothesis given that one exists.