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What is Limits of confidence of a hypothesis determined by? and explain in detail?
Ans. is 'd' i.e., 1-Level of significance First read about these different terms : ? Confidence interval It is the interval within which a parameter value is expected to lie with ceain confidence levels, as could be revealed by repeated samples. o It is the interval (range) around the mean of population in which the means of multiple samples of same population are dispersed. o If independent samples are taken repeatedly from the same population, and a confidence interval is calculated, then a ceain percentage (confidence level) of the intervals will include the unknown population parameter. o For example 95% of sample means will be covered by 2SD from population mean here. Confidence level --> 95%. 95% confidence interval for population mean --> Mean +- 2SD. o A narrow confidence interval is always preferable as it tells more precisely about the population mean:-- i) Large the sample size, narrower the confidence interval. ii) Smaller the Standard detion, narrower the confidence interval. Confidence limits o Are the upper and lower boundries of confidence interval, i.e., the values which define the range of confidence interval. Confidence limits is calculated by mean and standard detion. I am giving a very simple example : ? o If mean weight of a sample of children in a school is 30 Kg and SD is 1. Then. i) Confidence interval = Mean +- 2SD = 30 +- 2 = 28 to 32 kg. ii) Confidence level = 95% (that means 95% of values will be covered under the range 38 to 32). iii) Confidence limit = 28 (lower limit) and 32 (upper limit) Level of significance Level of significance is the criterian used to rejecting null hypothesis, i.e., to find out significant difference between two variable. o In simple words, it is defined as the probability of making a decision to reject the null hypothesis. o The decision is often made by using p value, i.e., p value denotes significance level. P vlalue 0.01 means that there is 99% of probability of rejecting null hypothesis when it is false, that is there is significant difference between two variable. o The significance level is usually set at 0.05 (p=0.05). The smaller the p-value (significance level), the more significant the result said to be. Now explanation for this question is : ? Confidence intervals are closely related to statistical significance testing. In many situations, if the point estimate of parameter is 'X', with confidence interval `a-b' at confidence level P, then any value outside this interval (a-b) will be significantly different from X at significance level a =1 - P under the same distributional assumption that were made to generate the confidence interval. o That means, if in an estimtion of second parameter we obsrved a value less than 'a' or greater than 'b' we would reject null hypothesis that the true value of this parameter equaled 'X' at the level of significance. o Conversely, if the estimate of second parameter lay within the interval `a-b', we would be unable to reject the null hypothesis that the parameter equaled 'X'. In consequence, if the estimates of two parameters have a confidence interval at a given P value that do not overlap, it is very likely that the two values are significantly different at the corresponding value of a.