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CONFIDENCE INTERVAL
• It is the interval or range of values which most
likely encompasses the true population value.
• It is the extent that a particular sample value
deviates from the population
• A range or an interval around the sample value
• Range or interval is called confidence interval.
• Upper & lower limits are called confidence limits.
TESTING THE STATISTICAL
HYPOTHESIS
• Null hypothesis or hypothesis of no
difference (Ho)
• Alternative hypothesis of significant
difference (H‫)׀‬
• Test of significance to accept or reject
hypothesis
• A zone of acceptance
• A zone of rejection
Testing of hypothesis
• Z- test when sample is more than 30
• T-test when sample is less than 30
• Chi square test when the data is in
proportions
TYPE 1 ERROR
• Null hypothesis of no difference is rejected
when estimate falls in the zone of
acceptance at 5 % level.
• We are changing the level of significance
from 5% to 6,7,8 or 10%.
• It is called type 1 error.(ά)
TYPE II ERROR
• Ho is accepted when it should been
rejected because the estimate falls in the
zone of rejection.
• We are changing the level of acceptance
from 5% to 4,3,2 or 1% level of
significance.
• This is committing of type II error or β
error.
ERROR
• Type I=Ho is true but it is rejected.
• Type II= Ho is false but it is accepted.
Inference
Accept it
Reject it
Hypothesis is
true
Correct
decision
Type I error
Hypothesis is
false
Type II error
Correct
decision
Minimize Errors
• Take as large a random sample as
possible and interpret the results at
5% i.e. critical level of significance.
TESTS OF SIGNIFICANCE
• Mathematical methods by which
probability (p) or relative frequency of an
observed difference, occurring by chance
is found.
• It may be a difference between means or
proportions of sample and universe or
between estimates of experiment and
control group.
Stages for tests
• State the null hypothesis of no or chance
difference
• State the alternative hypothesis
• Determine P value i.e. probability of
occurrence of estimate by chance i.e.
accept or reject hypothesis. (the distance from
the mean at which Ho is rejected is called level of
significance).
• Draw conclusion on the basis of p value.
• The difference observed is due to chance
or play of some external factors on the
sample under study.
STANDARD ERROR
• Standard error is the standard deviation of the
means of different samples of population.
• Standard error is the measure of chance
variation.
• S.E. is a measure which enables to judge
whether a mean of a given sample is within the
set of confidence limits or not, in a population.
• S.E= SD/√n (it is the SD of the sample divided
by the square root of number of observations in
the sample).
Uses of SE
• To work out the limits of desired
confidence within which population mean
will lie.
• To determine whether the sample is drawn
from a known population or not.
• To find SE of difference b/w two means to
know the difference is real, statistically
significant or insignificant due to chance.
• To know the size of sample.
Confidence limits
• SBP of a random sample of 566
students were taken, mean BP was
128 mm and standard deviation is
13.05mm. Find 95% confidence limits
of BP within which the population
mean would lie?
Confidence limits
• SBP of a random sample of 566
students were taken, mean BP was
128 mm and standard deviation is
13.05mm. Find 95% confidence limits
of BP within which the population
mean would lie?
• SE=0.55
Confidence limits
• SD of blood sugar level in a
population is 6 mg %. If population
mean is not known, within what limits
is it likely to lie if a random sample of
100 has a mean of 80 mg %?
Confidence limits
• In a population sample of children
with mean height of 66 cm and
SD=2.7 cm, can a sample of 100 with
a mean of 67cm occur easily? If you
find that the probability is low
(P<0.01), what does it indicate?
Sample size
• L= 2 σ
√n
√n= 2 σ
L
n= 4 σ²
L²
Example:
1.mean pulse rate=70
Pop. Standard deviation(σ)=8 beats
Calculate sample size?
2. Mean SBP=120,SD=10, calculate n?
Sample size
• Qualitative data
• N=4pq
L²
e.g.