Question

To test the efficacy of three different brands of fertilizer, you grow seedlings on each of the brands, plus a control with no fertilizer, for a total of four treatments. At the end of two months, you weigh each seedling.

Here are the data, in grams:

fertilizer A	fertilizer B	fertilizer C	control
12	15	11	9
15	16	13	11
11	14	17	10
14	18	14	13
12	18	12	9
14	13	14	11

The question of interest is whether fertilizer affects plant growth. Work through the 10 steps on your own, then answer the questions in this module.

Step 2: What is the null hypothesis?

• A.

  All μi are equal.

• B.

  Not all μi are equal.

Step 3: What is the alternative hypothesis?

• A.

  All μi are equal.

• B.

  Not all μi are equal.

Step 4: What is α?

• A.

  α=0.05 and extremely small values of FOBS in the left tail of the F distribution will reject H₀.

• B.

  α=0.05 and extremely large values of FOBS in the right tail of the F distribution will reject H₀.

• C.

  α/2=0.025 and extreme values of FOBS in either tail of the F distribution will reject H₀.

Step 5: Which statistical test are you using?

• A.

  χ2 Contingency table test

• B.

  χ2 Intrinsic Goodness of Fit test

• C.

  χ2 Extrinsic Goodness of Fit test

• D.

  ANOVA

• E.

  Tukey's Honestly Significant Difference test

• F.

  Bonferroni's t-test

Recall that:

SSTRT=∑i=1kni(X¯i∙−X¯∙∙)2

What is SSTRT? For "internal" calculations like this one, give your answer to four decimal places.

For this experiment, SSERR=66.3333.

What is SSTOT? Give your answer to four decimal places.

To complete the next steps, fill out the ANOVA table on your own.

Source	df	SS	MS	F	p
TRT
ERR				empty	empty
TOT			empty	empty	empty

Step 6: What is the F statistic? Give your answer to two decimal places.

Step 7: What is FCRIT? Give your answer to two decimal places.

Step 8: How does FOBS compare to FCRIT?

• A.

  FOBS>FCRIT and in the critical tail.

• B.

  FOBS<FCRIT and in the critical tail.

• C.

  FOBS>FCRIT and not in the critical tail.

• D.

  FOBS<FCRIT and not in the critical tail.

Steps 9 & 10: Do you accept or reject H₀, and what do you conclude? Select all that are correct.

• A.

  Accept

• B.

  Reject

• C.

  Fertilizer treatment affects plant growth.

• D.

  Fertilizer treatment does not affect plant growth.

Answer 1

using data>data >analysis>One Way ANOVA

we have

Anova: Single Factor
SUMMARY
Groups	Count	Sum		Average	Variance
fertilizer A	6	78		13	2.4
fertilizer B	6	94		15.66667	4.266667
fertilizer C	6	81		13.5	4.3
control	6	63		10.5	2.3
ANOVA
Source of Variation	SS	df		MS	F	P-value	F crit
TRT	3	81		27	8.140704	0.000973	3.098391
ERR	20	66.33333		3.316667
Total	23	147.3333

Step 2: the null hypothesis is

• A :All μi are equal.

Step 3: the alternative hypothesis is

• B.Not all μi are equal.

Step 4:

• C. α/2=0.025 and extreme values of FOBS in either tail of the F distribution will reject H₀.

Step 5: statistical test are you using is

• D.ANOVA

What is SSTRT = 81

SSERR=66.3333.

What is SSTOT is 147.333.

To complete the next steps, fill out the ANOVA table on your own.

Source of Variation	SS	df		MS	F	P-value
TRT	3	81		27	8.140704	0.000973
ERR	20	66.33333		3.316667
Total	23	147.3333

Step 6: \the F statistic is 8.1407

Step 7: FCRIT is 3.0984

Step 8: How does FOBS compare to FCRIT?

• A.FOBS>FCRIT and in the critical tail.

Steps 9 & 10: Do you accept or reject H₀, and what do you conclude? Select all that are correct.

• B.

  Reject

• D.

  Fertilizer treatment does not affect plant growth.