Question: A researcher believes that treating seeds with certain additives before planting can enhance the growth of plants. An experiment to investigate this is conducted in a greenhouse. From a large number of Roma tomato seeds, 24 seeds are randomly chosen and 2 are assigned to each of 12 containers. One of the 2 seeds is randomly selected and treated with the additive. The other seed serves as a control. Both seeds are then planted in the same container. The growth, in centimeters, of each of the 24 plants is measured after 30 days. These data were used to generate the partial computer output shown below. Graphical displays indicate that the assumption of normality is not unreasonable.

1. Construct a 95% confidence interval for the mean difference in growth in centimeters, of the plants from the untreated and treated seeds. Interpret this interval.
2. What assumptions must be made in order to construct a statistically valid confidence interval in part (a)?
3. Based only on the confidence interval in part (a) is there sufficient evidence to conclude that there is a significant difference in growth of the plants from untreated seeds and the plants from treated seeds? Justify your conclusion.
4. Now conduct a hypothesis test to see if growth of seeds with additive is larger than growth of seeds without additive is significant at the .01 level. Show your work.

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