Final answer:
The correct standard error of the distribution of the difference in means (SE) after calculating and rounding to two decimal places is 0.84, which corresponds to option (B).
Step-by-step explanation:
The student is asking about the standard error of the difference in means (SE) for two independent samples. Here, we have two samples with sizes of 30 and 90, and both have a standard deviation of 3 initially. When 30 values are added to the first sample, its standard deviation doubles. The calculation of SE involves combining the standard errors of both samples.
For the first sample (n1 = 60 after adding 30 values), the standard deviation doubles to 6. Its standard error (SE1) is therefore 6 / sqrt(60). For the second sample (n2 = 90), the standard error (SE2) is 3 / sqrt(90).
The overall standard error for the distribution of the difference in means can be calculated using
SE = sqrt(SE1^2 + SE2^2).
Plugging in the values, we have:
SE1 = 6 / sqrt(60) = 0.7746
SE2 = 3 / sqrt(90) = 0.3162
SE = sqrt(0.7746^2 + 0.3162^2) = sqrt(0.6000 + 0.1000) = sqrt(0.7000)
SE = 0.83666, which rounded to two decimal places is 0.84.
The correct answer from the options provided is (B) 0.84.