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. InferenceAccept itReject it Hypothesis is true Correct decision Type I error Hypothesis is false Type II errorCorrect 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.