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p-value-ex-3123

p-value-ex-3123 - 6 H a µ> 240 versus H o µ< 240 If n...

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Observed Significance Level (P-value) The observed significance level , or P-value , for a specific statistical test is the probability (assuming the null hypothesis is true) of observing a value of the test statistic that is at least as contradictory to the null hypothesis, and supportive of the alternative hypothesis as the actual one computed from the sample data. P-value Calculation Exercises For each test of hypothesis, compute the p-value. Sketch a figure. 1) H a : µ > 240 versus H o : µ < 240 If n = 85 and z = 2.35, find the p-value of z = 2.35. 2) H a : µ < 100 versus H o : µ > 100 If n = 150 and z = -2.78, find the p-value of z = -2.78. 3) H a : µ = / 75 versus H o : µ = 75 If n = 62 and z = -2.23, find the p-value of z = -2.23 4) H a : µ < 100 versus H o : µ > 100 If n = 20 and t = -1.78, find the p-value of t = -1.78. 5) H a : µ = / 75 versus H o : µ = 75 If n = 22 and t = -2.236, find the p-value of t = -2.236.
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Unformatted text preview: 6) H a : µ > 240 versus H o : µ < 240 If n = 18 and t = 2.354, find the p-value of t = 2.354. Decision Criterion for a Hypothesis Test Using the P-value: If the P-value is less than α , reject the null hypothesis; otherwise, fail to reject the null hypothesis. Example: H a : µ =/ 30 H o : µ = 30 Assumptions: Since n > 30, the sampling distribution of x ¯ is approximately normally distributed. Test Statistic: If σ is not known, use s for σ . α = .05 RR: p-value < .05 Calculation: z = -1.54 P-value = 2P(z > z calculated ) = 2P(z > 1.54) = 2P(z < -1.54) = 2(.5 - .4382) = 2(.0618) = .1236 Decision: Fail to reject H o . Conclusion: The data do not provide enough evidence to conclude that the population’s mean differs from 30....
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