9.3 Students in 3 treatment groups (no fertilizer, liquid fertilizer, pellet fertilizer) in a class monitored and recorded the number of days that it took until they could perform the first pruning for their basil plant. SPSS output containing statistics about the number of days required is provided for the LIQUID group and the PELLET groups below. Perform a two independent samples t test to determine if there is a significant difference between the days to first pruning in the liquid fertilizer and pellet fertilizer groups. Let a = 5%. SPSS Output: Summary Statistics Group Statistics TREATMENT N Mean Std. Deviation S.E. Mean PRUNEL LIQUID PELLET Hypotheses: (2m) 36.50 35.20 3.71 182 41 PAGE 4 Test statistic(2m): (4-4)-(4-4) Assumptions(4m): 1 2 3. 4. (1m) Df: formula -rounded down to near integer Verify that df =27.64 (round down to 27) Critical Region (2m): On a test, you would use min (n1-1, n2 -1) = mo(19,19) = 19 For this assignment, use 27. Decision/Why: (2m): (2m) P-value statement: Exact value from statdistributions.com: Bracketed from t tables: Confidence Interval(2m): Decision/Why: (2m) (Highlight correct answers) Since our value ( ) 0.05, we (reject, fail to reject) Ho. Decision/Why (2m): (Highlight correct answers): The confidence Interval (contains, does not contain 0), so at the 5% level of significance, there (is, is not) significant evidence that there is a difference in the number of days to first pruning for the liquid fertilizer and pellet fertilizer groups. 9.4 For each of the following, answer the question and give a short explanation of your reasoning. (a) (1m) A 95% confidence interval for the difference between two means is reported as (0.8, 2.3). What can you conclude from results of a significance test that the population means are equal versus the two-sided alternative? As both limits are positive, so we can conclude that there is significant difference between two population means (b) (1m) Will larger samples give a larger or smaller margin of error for the difference between two sample means? Recall that the margin of error is the amount that follows the +/- sign in a confidence interval Larger the sample size, smaller the standard error, so smaller the margin of error (c) (1m) A 10% significance test for comparing two means is performed. The test statistic is t=-1.521 with 15 degrees freedom. Can you reject the null hypothesis that the population means are equal versus the two-sided alternative that they are unequal? Why or why not? 1.521 df-15 p-value(two tailed)-tdist(1.521,15,2)=0.1491 ASR value>0.1,we fail to reject the null hypothesis. We can not reject the null hypothesis that the population means are equal. (d) (1m) A 10% significance test for comparing two means is performed. The test statistic ist=-1.521 with 15 degrees freedom. Can you reject the null hypothesis that the two populations are equal versus the one-sided alternative that the difference between the means is negative? Why or why not? 1.521 df-15 p-value=tdist(1.521,15,1)=0.0745 ASR value