Question

2. A fourth grade class is studying the environment. One of the assignments is to grow bean plants in different soils. Tommy chose to grow his bean plants in soil found outside his classroom mixed with dryer lint. Tara chose to grow her bean plants in potting soil bought at the local nursery. Nick chose to grow his bean plants in soil from his mother's garden. No chemicals were used on the plants, only water. They were grown inside the classroom next to a large window. Each child grew five plants. At the end of the growing period, each plant was measured, producing the data (in inches). Does it appear that the three media in which the bean plants were grown produce the same mean height? Test at a 2.5% level of significance. Tommy's Plants Tara's Plants Nick's Plants 24 25 21 31 27 23 22 30 20 23 20 1. Extract information: (Round to found decimal places if necessary) (Find variance between samples ns and mean of the sample variances S, by calculator) 23 23 30 28 2. Original Claim: 3. State the null and alternative hypotheses. 4. Distribution (Graphically): 5. Find the df of numerator, df of denominator and Critical value(s): 6. Compute the value of test statistic. (Show the formula and all your work) (Round to four decimal places) 7. Statistical Conclusion: 8. Final words:

Answer 1

Claim: The three media in which the bean plants were grown produce the same mean height.

The hypothesis being tested is:

H₀: µ₁ = µ₂ = µ₃

H_a: At least one means is not equal

The output is:

	Mean	n	Std. Dev
	24.2	5	3.42	Tommy's Plants
	25.4	5	4.28	Tara's Plants
	24.4	5	4.04	Nick's Plants
	24.7	15	3.68	Total
ANOVA table
Source	SS	df	MS	F	p-value
Treatment	4.13	2	2.067	0.13	.8760
Error	185.20	12	15.433
Total	189.33	14

df of numerator = 2, df of denominator = 12, critical value = 3.89

The test statistic is 0.13.

The graph is:

Comparison of Groups 1. Tommy's Plants Tara's Plants Nick's Plants

The p-value is 0.8760.

Since the p-value (0.8760) is greater than the significance level (0.05), we cannot reject the null hypothesis.

Therefore, we have insufficient evidence to conclude that the three media in which the bean plants were grown produce the same mean height.

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