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Unformatted text preview: 1 9 Tests of Hypotheses for a Single Sample Hypothesis testing for the mean, variance unknown (small samples) continued Tests for variance and std. dev. Tests for proportion OUTLINE Lecture 25 12/02/11 P-value for a t test The P value of a t-test is just the smallest level of significance at which the null hypothesis would be rejected ( It is the tail area beyond the value of the test statistic t for a one sided test or twice this area for a two sided test). P-value for a t test Since the t table in the Appendix only contains 10 critical values for each t distribution, computation of exact P value directly from the table is usually impossible. However, it is possible to find the upper and lower bounds on the P value from this table Obtaining P values Suppose we calculate t = 2.22 for a one-tailed test from a sample size of 6. df = n 1 = 5. 0.025 < P-value < 0.050 Suppose we calculate t = 2.72 for a two-tailed test from a sample size of 15 df = n 1 = 14. 2(0.005) < P-value < 2(0.01); Hence 0.01 < P-value < 0.02 Since P-value is twice this area for a two sided test Using P- values to Make a Decision Decision Rule Based on P- value To use a P- value to make a conclusion in a hypothesis test, compare the P- value with . 1. If P , then reject H . 2. If P > , then fail to reject H . 2 Testing Using P- values: Example 1 A manufacturer claims that its rechargeable batteries have an average life greater than 1,000 charges. A random sample of 10 batteries has a mean life of 1002 charges and a standard deviation of 14. Is there enough evidence to support this claim at = 0.01? H 1 : > 1000 (Claim) H : = 1000 The level of significance is = 0.01. The standardized test statistic is The degrees of freedom are d.f. = n 1 = 10 1 = 9....
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