Which of the following statements is true? a) A 95% confidence interval is narrower than a 90% confidence interval for the same set of data. b) Increasing the sample size will decrease the margin of error in your confidence interval. c) The critical value is the variance of the sampling distribution. d) The point estimate is the measure of variation used in the computation of the margin of error. e) Smaller sample sizes produce larger margins of error because smaller samples always have larger standard deviations.

The correct option is;

b)

Step-by-step explanation:

a) 95% Sample CI =  152.6395 to  153.3605; Range = 0.721 Wider

90%  Sample CI = 152.6975 to  153.3025; Range= 0.605 Narrower

b) Sample size ∝ 1/Error²

Therefore, increasing the sample will decrease the margin of error

c) The critical value is the value of the test statistic at the level of confidence

Variance = (Standard deviation)²

d) Point estimate is the mean or average, variation is the range or also the variance

e) Smaller samples have their relative standard deviations which does not depend on the sample size

∠acb = 8°

step-by-step explanation:

∠xba lies on the circle and is half the measure of the intercepted arc ax

hence

measure of arc ax = 2 × 42° = 84°

∠acb is outside the circle and is

∠acb = (arcab - arcax ), hence

∠acb = 0.5 (100 - 84) = 0.5 × 16° = 8°

f(x) = - 2/3x + 5; f(5/2)

substitute 5/2 in for x:

f(5/2) = -2/3(5/2) + 5

simplify the right side:

f(5/2) = -5/3 + 5

f(5/2) = 10/3

answer:

f(5/2) = 10/3

i hope this you!