A regression of y = sunburn index for a pea plant on x = distance from an ultraviolet light source was considered in Exercise 13.22. The data and summary statistics presented there give

a. Calculate a 95% confidence interval for the true average sunburn index when the distance from the light source is 35 cm.

b. When two 95% confidence intervals are computed, it can be shown that the simultaneous confidence level is at least [100 − 2(5)]% = 90%. That is, if both intervals are computed for a first sample, for a second sample, yet again for a third, and so on, in the long run at least 90% of the samples will result in intervals both of which capture the values of the corresponding population characteristics. Calculate confidence intervals for the true mean sunburn index when the distance is 35 cm and when the distance is 45 cm in such a way that the simultaneous confidence level is at least 90%.

c. If two 99% intervals were computed, what do you think could be said about the simultaneous confidence level?

d. If a 95% confidence interval were computed for the true mean index when x = 35, another 95% confidence interval were computed when x = 40, and yet another one when x = 45, what do you think would be the simultaneous confidence level for the three resulting intervals?

e. Return to Part (d) and answer the question posed there if the individual confidence level for each interval were 99%.

Data from Exercises 22

The article “Effects of Enhanced UV-B Radiation on Ribulose-1,5-Biphosphate, Carboxylase in Pea and Soybean” (Environmental and Experimental Botany [1984]: 131–143) included the accompanying data on pea plants, with y = sunburn index and x = distance (cm) from an ultraviolet light source.

Estimate the mean change in the sunburn index associated with an increase of 1 cm in distance in a way that includes information about the precision of estimation.

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n = 15 b = -.0565 x = 40.60 a = 4.500 (xx)² = 3311.60 SSResid= .8430