HWK_9_Soln

Histogram of diffs diffs Frequency 0.4 0.5 0.6 0.7 0.8 0.9 0.0 0.5 1.0 1.5 2.0 -1.0 0.0 1.0 0.4 0.5 0.6 0.7 0.8 Normal Q-Q Plot Theoretical Quantiles Sample Quantiles par( mfrow= c( 1 , 1 )) d. Does this data give us strong evidence that the mean carbohydrate concentration in the shoot is higher than that in the root? Conduct a matched-pair t test of the hypotheses: H o : μ S - μ R ≤ 0 (or H o : μ S - R ≤ 0 ) vs H A : μ S - μ R > 0 (or H A : μ S - R > 0 ). Compute the test statistic, degrees of freedom, and p value “by hand”. Check your answers using t.test(). Draw a conclusion in the context of the question at a 1% significance level. Test Statistic Degrees of Freedom p-value Test Statistic: 9.557162, df=5, pvalue: 0.0001061668. We have strong enough evidence at the 1% level to reject the null. Evidence suggests that the mean carbohydrate concentration is more 0.2 higher in the shoot than the root of bean plants. (sd(diffs)/sqrt(length(diffs))) ## [1] 0.06400087 ( t_obs= (mean(diffs)- 0 )/(sd(diffs)/sqrt(length(diffs)))) #9.557162 ## [1] 9.557162 ( 1 -pt(t_obs, df= length(diffs)- 1 )) #0.0001061668 ## [1] 0.0001061668 t.test(Shoot, Root, mu= 0 , paired= TRUE, alternative= "greater" ) ## ## Paired t-test ## 3