RVUC- Statistics Short Note (2).doc

# Ninety five percent of the sample means selected from

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Ninety-five percent of the sample means selected from a population will be within 1.96 standard deviations of the population mean . Ninety-nine percent of the sample means will lie within 2.58 standard deviations of the population mean. Critical values of Z and t 10

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11 | P a g e Confidence level& Confid. Interval 11
12 | P a g e Region of Rejection It is also called critical region. - If the test statistic falls within the region of rejection, then, the Ho is rejected. - It is a set of values of the test statistic for which the null hypothesis is rejected in a hypothesis test. Region of acceptance The set of values within the region of acceptance. - If test statistic falls in the acceptance region, then we accept Ho. Two forms of Testing hypothesis Based on the form of the null hypothesis and alternative hypothesis, testing hypothesis takes two forms i.e. a one tailed test and two tailed test. One- tailed test - It is a test of a statistical hypothesis, where the region of rejection is on only one side of the sampling distribution on the normal curve. Example: Suppose the null hypothesis states that the mean is less than or equal to 10. The alternative hypothesis would be that the mean is greater than 10. A one tailed test is one in which the alternative hypothesis is directional ; unlike a two – tailed test which does not specify direction NB: A one-tailed test can be: a) a right- tailed (upper-tailed test) b) a left- tailed (lower- tailed test) Right- tailed (sided) test Rejection region will be on the right tail of the curve. Right Z (α ) Will reject the null hypothesis if the sample statistic (calculated value) is significantly higher than the hypothesized population parameter (table value). 12

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13 | P a g e Note in the chart that: 1. The area where the null hypothesis is not rejected is to the left of 1.65. The area of rejection is to the right of 1.65. 2. A one-tailed test is being applied. 3. The .05 level of significance was chosen. 4.The sampling distribution of the statistic z is normally distributed. 5. The value 1.65 separates the regions where the null hypothesis is rejected and where it is not rejected. 6. The value 1.65 is the critical value. A left- tailed test - rejects the null hypothesis if the sample statistic is significantly lower than the hypothesized population parameter. Z on left tail z (1-α ) - Ha has a less than (<) sign - rejection region is at the left tail. A normal distribution curve for left tailed test at alpha 0.05 (i.e. 5% significance level in Z- statistic) 13
14 | P a g e Two-tailed test is a test of a statistical hypothesis, where the region of rejection is on both sides of the sampling distribution. Example: suppose the null hypothesis states that the mean is equal to 10. The alternative hypothesis would be that the mean is different from 10 .

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