Let ˆθ be a statistic that is normally distributed with mean θ and standard error σθˆ. Show that 100(1 − α)% confidence interval for θ is given by: ˆθ ± z α 2 σθˆ

Step-by-step explanation:

We are given the following in the question:

is distributed normally.

Mean =

Standard error =

Significance level =

Thus, the confidence percentage is

Confidence interval:

Putting the values, we get,

which is the required confidence interval.

i understand 100% 10/10 hit or miss?

step-by-step explanation:

  b.   the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

so the change in y-value for function f is (6 )) = 9.

the table tells us

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).