Answer to Question #335308 in Statistics and Probability for rose

Question

the average height of randomly chosen 45 female students was 155cm. with standard deviation of 3.5 cm find the 95% confidence interval

Answer 1

The formula to calculate a confidence interval for a population mean is as follows:

$CI=\bar{x}\pm z\cdot\cfrac{s}{\sqrt{n}},$

where:

• $\bar{x}=155$ : sample mean
• z: the chosen z-value, for a 95% confidence interval z = 1.960
• $s=3.5$:  sample standard deviation
• n = 45:  sample size.

So,

$CI=155 \pm 1.960\cdot\cfrac{3.5}{\sqrt{45}}=\\= 155\pm1.02=(153.98, 156.02).$