there enough evidence to support the claim? Use the value approach. (a) Setup : 25.4 µ = : (left-tailed test) µ<25.4 (b) Use StatCrunch to find and its correspondingvalue. Hypothesis test results: μ : Mean of population H0 : μ = 25.4 HA : μ < 25.4 Mean Sample Mean Std. Err. DF T-Stat P-value μ 22.1 1.06 24 -3.1132075 0.0024 (c) Conclusion.: = -3.113; P-value 0.0024. Since P-value (0.0024) < reject the . There is ≈ α, sufficient evidence to support the claim that the commute time in his city is less than executive’s 25.4 minutes. Example 4: Michael Sullivan, son of the author, decided to enroll in a reading course that allegedly increases reading speed and comprehension. Prior to enrolling in the class, Michael read 198 words per minute (wpm). The following data represent the words per minute read for 10 different passages read after the course. (a) Because the sample size is small, we must verify that reading speed is normally distributed and the sample does not contain any outliers. Perform a normal probability plot (QQ plot) and a boxplot. Are the conditions for testing a hypothesis satisfied? The boxplot indicated there are no outliers. The QQ plot indicated the sample data may have come from a population that is normally distributed because all observed data are close to the straight line. The t-hypothesis testing conditions are satisfied. (b) Was the class effective? Use the level of significance. (i) Setup : = 198 µ : 198 (a right-tailed test) µ> (ii) Use StatCrunch to find and its correspondingvalue. Open StatCrunch Stats T Stats one sample with data select var1 select → → → → → → Hypothesis test forµ :µ = 198, : 198 compute µ> → → Hypothesis test results: μ : Mean of variable
there enough evidence to support the claim? Use the value approach. (a) Setup : µ = 25.4 : µ<25.4 (left-tailed test) (b) Use StatCrunch to find and its correspondingvalue. Hypothesis test results: μ : Mean of population H0 : μ = 25.4 HA : μ < 25.4 Mean Sample Mean Std. Err. DF T-Stat P-value μ 22.1 1.06 24 -3.1132075 0.0024 (c) Conclusion.: = -3.113; P-value ≈ 0.0024. Since P-value (0.0024) < α, reject the . There is sufficient evidence to support the executive’s claim that the commute time in his city is less than 25.4 minutes. Example 4: Michael Sullivan, son of the author, decided to enroll in a reading course that allegedly increases reading speed and comprehension. Prior to enrolling in the class, Michael read 198 words per minute (wpm). The following data represent the words per minute read for 10 different passages read after the course. (a) Because the sample size is small, we must verify that reading speed is normally distributed and the sample does not contain any outliers. Perform a normal probability plot (QQ plot) and a boxplot. Are the conditions for testing a hypothesis satisfied? The boxplot indicated there are no outliers. The QQ plot indicated the sample data may have come from a population that is normally distributed because all observed data are close to the straight line. The t-hypothesis testing conditions are satisfied. (b) Was the class effective? Use the level of significance. (i) Setup : µ = 198 : µ> 198 (a right-tailed test) (ii) Use StatCrunch to find and its correspondingvalue. Open StatCrunch → Stats → T Stats → one sample → with data → select var1 → select Hypothesis test forµ → :µ = 198, : µ> 198 → compute Hypothesis test results: μ : Mean of variable