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:

fertilizerA fertilizerB fertilizerC 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 i are equal.
• B.
• Not all i are equal.

Step 3: What is the alternative hypothesis?

• A.
• All i are equal.
• B.
• Not all i are equal.

Step 4: What is ?

• A.
• =0.05 and extremely small values of FOBS in the left tail of the F distribution will reject H₀.
• B.
• =0.05 and extremely large values of FOBS in the right tail of the F distribution will reject H₀.
• C.
• /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.
• 2 Contingency table test
• B.
• 2 Intrinsic Goodness of Fit test
• C.
• 2 Extrinsic Goodness of Fit test
• D.
• ANOVA
• E.
• Tukey's Honestly Significant Difference test
• F.
• Bonferroni's t-test

Recall that:

SSTRT=i=1kni(XiX)2

What is SSTRT? For "internal" calculations like this one, give your answer tofourdecimal 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.

SourcedfSSMSFpTRTERRemptyemptyTOTemptyemptyempty

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
• C.
• FOBS>FCRIT and not in the critical tail.
• D.
• FOBS

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.