If p > α , Statement: If p < the p-value (< or >) I (reject or fail to reject) the H0. There (is or is α, “Since α, not) sufficient evidence to suggest that Ha.” Facts about p-values: Drinking water is considered unsafe if the mean concentration of Example 5: lead is greater than 15 ppb (parts per billion). Suppose a community randomly selects of 25 water samples and computes a z-test statistic of 2.1. (Assume lead concentrations are normally distributed.) Write the hypotheses, calculate the & write the appropriate conclusion for = 0.05. α At level of .05, would you reject or fail to reject the H0? an α a) .03 b) .15 c) .45 d) .023 Calculating p-values: For z-test statistic - A certain type of frozen dinners states that the dinner contains 240 Example 6: calories. A random sample of 12 of these frozen dinners was selected from to see if the caloric content was greater than stated on the box. The z-test statistic was calculated to be 1.9. Assume calories vary normally. Write the hypotheses, Draw & shade the curve & calculate the p-value: calculate the p-value & write the appropriate conclusion = 0.05. for α 1) right-tail test z = 1.6; n = 20 2) left-tail test z = -2.4; n = 15 Test statistic formulas: z-test: 3) two-tail test z = 2.3; n = 25 Writing Conclusions:
If p > α , If p < α, Facts about p-values: At an α level of .05, would you reject or fail to reject the H0? a) .03 b) .15 c) .45 d) .023 Calculating p-values: For z-test statistic - Draw & shade the curve & calculate the p-value: 1) right-tail test z = 1.6; n = 20 2) left-tail test z = -2.4; n = 15 3) two-tail test z = 2.3; n = 25 Writing Conclusions: Statement: “Since the p-value (< or >) α, I (reject or fail to reject) the H0. There (is or is not) sufficient evidence to suggest that Ha.” Example 5: Drinking water is considered unsafe if the mean concentration of lead is greater than 15 ppb (parts per billion). Suppose a community randomly selects of 25 water samples and computes a z-test statistic of 2.1. (Assume lead concentrations are normally distributed.) Write the hypotheses, calculate the & write the appropriate conclusion for α = 0.05. Example 6: A certain type of frozen dinners states that the dinner contains 240 calories. A random sample of 12 of these frozen dinners was selected from to see if the caloric content was greater than stated on the box. The z-test statistic was calculated to be 1.9. Assume calories vary normally. Write the hypotheses, calculate the p-value & write the appropriate conclusion for α = 0.05. Test statistic formulas: z-test: