Let a
and
b
stand for two different rational numbers. If ∣∣∣∣>∣∣∣∣
a
>
b
, then what else must be true?

CLEAR CHECK

a
is less than
b
.

On a number line,
a
is to the right of
b
.

a
is farther from 0
0
than
b
is.

The opposite of
a
is less than the opposite of
b
.

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.