Researchers studied the effect of a houseplant fertilizer on radish sprout growth. They randomly selected some radish seeds to serve as controls, while others were planted in aluminum planters to wich fertillizer sticks were added. Other conditions were held constant between the two groups. The following information shows data on the heights of plants (in cm) two weeks after germination. Use a t test to investigate whether the fertilizer has an effect on average radish sprout growth. Use alfa=0.05. CONTROL: n=28, ybar=2.58, s=0.65. FERTILIZED: n=28, ybar= 2.04, s= 0.72. Test the appropriate hypothesis to conclude whether height differed between the control and fertilized samples.

1) State your null and alternate hypotheses in equation form.

2) Evaluate your hypothesis by using the confidence interval method, i.e. compute a 95% confidence interval and evaluate it against the hypothesized mean as discussed in lecture. Based on this method alone, write your conclusion (reject or fail-to-reject) about the null hypotheses, and also state which hypothesis the evidence better supports and why.

3) Evaluate your hypothesis using the tcalc vs. tcrit method with =0.05, i.e. compute your test statistic (tcalc) and evaluate it against tcrit as discussed in lecture. Based on this method alone, write your conclusion (reject or fail-to-reject) about the null hypotheses, and also state which hypothesis the evidence better supports and why.

4) The P-value for this problem is less than 0.005 (0.005%). Evaluate this P-value against an =0.005, as discussed in lecture. Based on this method alone, write your conclusion (reject or fail-to-reject) about the null hypotheses, and also state which hypothesis the evidence better supports and why.

5) What is the proper interpretation of the P-value from part d? Your answer should mention both the null hypothesis and the sample that was obtained.

6) Did all three methods give you the same resulting conclusion about your null hypothesis? If so, was this expected or unexpected and state why it was expected or unexpected? If not, why do you believe you got differing answers?

7) One assumption of the test you just performed is that the population of MBF levels is normally distributed for both samples. The Shapiro-Wilk P-value for the control sample is 0.196, and is 0.170 for the fertilized sample. Did we violate the assumption of normality? How have you made this determination?

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