Question

Fresh St. Market grows tomatoes in two separate fields, in Richmond and downtown Vancouver. When tomatoes are ready to be picked, they get curious and want to know whether the sizes of the tomatoes differ between the two fields. They take a random sample of plants from each field and measure the heights of the plants. Here is a summary of the results. (Significance level 5%)

	Field A	Field B
Mean	1.3	1.6
sample standard deviation	0.5	0.3
Number of plants	22	24

1. Do you think the data supports any change in size of the tomatoes? (3 marks)
2. What is the 90% confidence interval of the difference in tomato sizes? (3 marks)

Answer 1

Let e la population mean of of tott tomaten totet tomatoes size for field A. Uz - population mean of tomatoes size toy field B X = 1.3 X2 = 1.6 si - os 52 = 0.3 n2 =24 ni= 22 dao.os There is no change in size of tomatoes. Ho He: There is change in size of tomato es. ie. Ho: M, =la vis Hi: 4, 742 test statistica tial = x, -22 ~ tnitna-2 ni O 1:3-06 .38 V 22 24

-0.3 tral = Jo.0114 +0.00375 -0-3 Vooolsis -0.3 0.1231 teal = -2.4370 df = nitha-2 = 22 +24-2 pvalue - Since Hi is two sided all t p-value = 2 P(tan> It call) - 2 P(t4472.4370) - 2 xo.oogs p-value = 0.019 Decision: p-value <&= 0.05 Reject Ho

Conclusion: There is a change is the size of tomatoes. goy confidence interval. &= 0.10 I = 0.05 t 44,0.05 = 1.68 margin of error (E) E = tu,oos x / 3 2 2 ni nz = 1.68x0.231 = 0.2068 E lower limit = (x,-%2) - E = -0.3 -0.2068 - Or 5068 Upper limità (81-72) te -0.3 + 0.2068 = -0.0932 90% confidence interval of the difference in tomato size is, (-0.5068 -0.0932)