# It is difficult to draw a line of demarcation between

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It is difficult to draw a line of demarcation between large and small samples; but a view among statistician is that, a sample is to be recorded as large only if its size exceeds 30 and if the sample size is less than 30, it is noted as small sample. The tests of significance used for large samples are different from the small samples, the reason being that the assumptions made in case of large samples do

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86 not hold good for small samples. The assumption that made in dealing with problems relating to large samples are : (a) the random sampling distribution of a statistic is approximately normal and (b) the values given by sample data are sufficiently close to the population values and can be used in their (population) place for calculating the standard error of the estimate. In case of small samples, the said above assumptions will no longer be hold good. It should be noted that the estimates will vary from sample to sample if we work with very small samples. We must satisfy with relatively wide confidence intervals. Of course, the wider the interval, the less is the precision. An inference drawn from inference based on a much smaller sample. Though, drawing a precise line of demarcation between the large sample and the small sample is not always easy, but the division of their theories is a very real one. As a rule, the theory and methods of small samples are applicable to large samples, but the reverse is not true. 9.4. REVISION POINT Accept Ho Reject Ho Ho True Ho False Correct decision Wrong decision Type II error Wrong decision Type I error Correct decision 9.5. INTEXT QUESTIONS 1) Explain the procedure for testing of hypothesis 2) Briefly Explain the importance of hypothesis testing in research 9.6. SUMMARY By the end of this lesson, you should be able to understand Hypothesis, null hypothesis, alternative hypothesis, type I error and type II error 9.7. TERMINAL EXERCISES 1) Which of the following statements about hypothesis tests is INCORRECT? a. H0 must always include equality. b. In a one- tailed test, H1 involves either “>” or “<“, but not “.”. c. If the test statistic lies in the rejection region, we reject the claim. d. The claim can be either H0 or H1. e. The critical value indicates the start of the rejection region. 2) A researcher wishes to compare the proportion of men and women who voted in the last federal election. Which of the following conclusion could NOT be drawn as the result of any hypothesis test. “At the given level of significance, we have evidence...” a) “... that the proportion of men who voted is larger than the proportion of women who Voted.” b) “... that the proportion of men who voted differs from the proportion of women who Voted.”
87 c) “... that the proportion of men who voted does not differ from the proportion of women Who voted.” d) “... that the proportion of men who voted is smaller than the proportion of women who Voted.” e) None of the above (each statement a-d is a possible conclusion).

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