Chapter+9

Chapter 9

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Unformatted text preview: 13­31 are not shown. Glow Two­Tailed Tests About a Population Mean: σ Known s Excel Value Worksheet A 1 Weight 2 6.04 3 5.99 4 5.92 5 6.03 6 6.01 7 5.95 8 6.09 9 6.07 10 6.07 11 5.97 12 5.96 B Sample Size 30 Sample Mean 6.1 Population Std. Dev. 0.2 Hypothesized Value 6 Standard Error 0.0365 Test Statistic z 2.7386 p -Value (lower tail) 0.9969 p -Value (upper tail) 0.0031 p -Value (two tail) 0.0062 Note: Rows 13­31 are not shown. C Glow Two­Tailed Tests About a Population Mean: σ Known Critical Value Approach 4. Determine the critical value and rejection rule. For α /2 = .03/2 = .015, z.015 = 2.17 Reject H0 if z < ­2.17 or z > 2.17 5. Determine whether to reject H0. Because 2.74 > 2.17, we reject H0. There is sufficient statistical evidence to infer that the alternative hypothesis is true (i.e. the mean filling weight is not 6 ounces). Glow Two­Tailed Tests About a Population Mean: σ Known Glow Critical Value Approach Sampling distribution x − µ0 z of = σ/ n Reject H0 Reject H0 Do Not Reject H0 α/2 = .015 ­2.17 α/2 = .015 0 2.17 z Confidence Interval Approach to Two-Tailed Tests About a Population Mean Select a simple random sample from the population x and use the value of the sample mean to develop the confidence interval for the population mean µ . (Confidence intervals are covered in Chapter 8.) If the confidence interval contains the hypothesized value µ 0, do not reject H0. Otherwise, reject H0. Confidence Interval Approach to Two-Tailed Tests About a Population Mean Glow The 97% confidence interval for µ is σ x ± zα / 2 = 6.1 ± 2.17(.2 30) = 6.1 ± .07924 n or 6.02076 to 6.17924 Because the hypothesized value for the population mean, µ 0 = 6, is not in this interval, the hypothesis­testing conclusion is that the null hypothesis, H0: µ = 6, can be rejected. Tests About a Population Mean: σ Unknown • Test Statistic x − µ0 t= s/ n This test statistic has a t distribution with n ­ 1 degrees of freedom. Tests About a Population Mean: σ Unknown s Rejection Rule: p ­Value Approach Reject H0 if p –value < α s Rejection Rule: Critical Value Approach H0: µ > µ 0 Reject H0 if t < ­tα H0: µ < µ 0 Reject H0 if t > tα H0: µ = µ 0 Reject H0 if t < ­ tα/2 or t > tα/2 p -Values and the t Distribution The format of the t distribution table provided in most statistics textbooks does not have sufficient detail to determine the exact p­value for a hypothesis test. However, we can still use the t distribution table to identify a range for the p­value. An advantage of computer software packages is that the computer output will provide the p­value for the t distribution. Example: Highway Patrol • One­Tailed Test About a Population Mean: σ Unknown A State Highway Patrol periodically samples vehicle speeds at various locations on a particular roadway. The sample of vehicle speeds is used to test the hypothesis H0: µ < 65 The locations where H0 is rejected are deemed the best locations for radar traps. Example: Highway Patrol Exam...
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This note was uploaded on 08/28/2011 for the course BUS 300 taught by Professor White during the Spring '09 term at Rutgers.

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