Question

18. A set of data has a sample mean of 65.4 and a standard deviation of 1.2. If the sample size is 45, what is the 99% confidence interval of this data?
A. 65.10 and 65.70
B. 65.33 and 65.47
C. 65.05 and 65.75
D. 64.94 and 65.86

Answer 1

Given:

Sample mean = 65.4

Standard deviation = 1.2

Sample size = 45

Confidence level = 99%

To find:

The confidence interval.

Solution:

The formula for confidence interval is

$CI=\overline{x}\pm z^*\dfrac{s}{\sqrt{n}}$

where, $\overline{x}$ is sample mean, z* is confidence value, s is standard deviation and n is sample size.

Confidence value or z-value at 99% = 2.58

Putting the given in the above formula, we get

$CI=65.4\pm 2.58\times \dfrac{1.2}{\sqrt{45}}$

$CI=65.4\pm 0.46$

$CI=65.4-0.46\text{ and }CI=65.4+0.46$

$CI=64.94\text{ and }65.86$

Therefore, the correct option is D.