In a study, we see that the average number of close confidants in a random sample of 2006 us adults is 2.2 with a standard deviation of 1.4 . if we want to estimate the number of close confidants with a margin of error within and with 90% confidence, how large a sample is needed? r

527

Step-by-step explanation:

Data provided in the question:

standard deviation, s = 1.4

Confidence level = 90%

Margin of error, E = 100% - 90% = 10% = 0.10

Now,

For 90% confidence level , the z value is = 1.64

also,

the relation for sample size and above data is given as

Sample size, n = [(z × s) ÷ E]²

or

n = [(1.64 × 1.4 ) ÷ 0.10]²

or

n = 527.16 ≈ 527

  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).

the answer

b. they are parallel and will never intersect.