Question

Question 5 A chemical engineering student did an experiment to determine the effect of three different pesticides on the yield of fruit tree from four different verities of citrus tree. The student selected randomly two trees in the farm from each variety. Then the three pesticides were assigned to one tree in each variety and the yield of fruit were obtained after the test period. The student want to see if there is any difference in the mean yield of fruits due to pesticides and different varieties of citrus fruit. Pesticide Variety A B C Type 1 48 39 50 Type 2 38 48 41 Type 3 53 55 67 a. State the null and alternative for the above problem. b. List the assumptions required for the above problem. c. Is there any significant difference in the mean yield of fruit due to pesticide type at 5% level of significance? d. Is there any significant difference in in the mean yield of fruit for different varieties of citrus fruit at 5% level of significance?

Please write the solution in a way that I can copy it

Answer 1

a. State the null and alternative for the above problem.

The hypothesis being tested is:

H0: µ1 = µ2 = µ3

Ha: Not all means are equal

b. List the assumptions required for the above problem.

• Normality – That each sample is taken from a normally distributed population.
• Sample independence – that each sample has been drawn independently of the other samples.
• Variance Equality – That the variance of data in the different groups should be the same.

c. Is there any significant difference in the mean yield of fruit due to pesticide type at 5% level of significance?

Source	SS	df	MS	F	p-value
Treatment	427.56	2	213.778	5.44	.0450
Error	236.00	6	39.333
Total	663.56	8

The p-value is 0.0450.

Since the p-value (0.0450) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that there is a significant difference in the mean yield of fruit due to pesticide type.

d. Is there any significant difference in in the mean yield of fruit for different varieties of citrus fruit at 5% level of significance?

Source	SS	df	MS	F	p-value
Treatment	69.56	2	34.778	0.35	.7173
Error	594.00	6	99.000
Total	663.56	8

The p-value is 0.7173.

Since the p-value (0.7173) is greater than the significance level (0.05), we fail to reject the null hypothesis.

Therefore, we cannot conclude that there is a significant difference in the mean yield of fruit for different varieties of citrus fruit.