Determine whether the series [infinity] ln(2n) 3n n=1 converges or diverges. SOLUTION The function f(x) = ln(2x) (3x) is positive and continuous for x > because the logarithm function is continuous. But it is not obvious whether or not f is decreasing, so we compute its derivative: f '(x) = 3x − 3 ln(2x) 9x2 = 3x2 .

The null and alternate hypotheses are: h0: μ1 ≤ μ2 h1: μ1 > μ2 a random sample of 22 items from the first population showed a mean of 113 and a standard deviation of 12. a sample of 16 items for the second population showed a mean of 99 and a standard deviation of 6. use the 0.01 significant level. find the degrees of freedom for unequal variance test. (round down your answer to the nearest whole number.) state the decision rule for 0.010 significance level. (round your answer to 3 decimal places.) compute the value of the test statistic. (round your answer to 3 decimal places.) what is your decision regarding the null hypothesis? use the 0.01 significance level.