And this last one
never mind i got it

List x1, x2, x3, x4 where xi is the midpoint endpoint of the five equal intervals used to estimate the area under the curve of f(x) between x = 0 and x = 10.

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.

Arandom sample of n = 25 observations is taken from a n(µ, σ ) population. a 95% confidence interval for µ was calculated to be (42.16, 57.84). the researcher feels that this interval is too wide. you want to reduce the interval to a width at most 12 units. a) for a confidence level of 95%, calculate the smallest sample size needed. b) for a sample size fixed at n = 25, calculate the largest confidence level 100(1 − α)% needed.