What would the 99% confidence interval be for the slope (i.e., light_intensity)?

Question

What would the 99% confidence interval be for the slope (i.e., light_intensity)? a. (0.0395, 0.0581) b. (0.0416, 0.0560) c. (0.0385, 0.0591) d. (0.0389, 0.0587) e. (0.0379, 0.0598) Continuing with the data from the problem above: Suppose that the prevailing scientific wisdom about goldenrod leaves is that the slope (i.e., light_intensity) should be 0.055. We want to know if the result of our regression model (0.0488) provides convincing evidence that the slope is different from 0.055. What is the T-statistic (or T-score) for the observed slope? What is the p-value associated with the T-statistic you obtained above? [Remember that this is a two-sided hypothesis test.] a. between 0.10 and 0.20 b. between 0.05 and 0.10 c. between 0.02 and 0.05 d. between 0.01 and 0.02

Explanation / Answer

a) here degree of freedom =n-2 =6

for 6 df and 99% CI, t=3.7074

sample mean =0.0488

and std error =0.002952

hence confidence interval =sample mean -/+ t*std error =0.0379 ; 0.0598

b) test stat t=(X-mean)/std error =(0.048806-0.055)/0.002952 =-2.0982

c) p value =0.0807

hence option b b/w 0.05 and 0.10

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