Question

The lifetime of a certain brand of battery is known to have a standard deviation of 9 hours. Suppose that a random sample of 90 such batteries has a mean lifetime of 38.9 hours. Based on this sample, find a 90% confidence interval for the true mean lifetime of all batteries of this brand.

Answer 1

Answer:

lower limit : 36.44

upper limit : 39.56

Step-by-step explanation:

Given :

s = 9

n = 90

x = 38.9

Alpha, α = 0.10

∴ $z_{\alpha/2}=z_{0.05} = 1.645$

The confidence interval is :

$=x \pm\left(z_{\alpha /2} \times \frac{s}{\sqrt{n}}\right)$

$=38.9 \pm\left(1.645 \times \frac{9}{\sqrt{90}}\right)$

$=38.9 \pm 1.56$

$=(36.44, 39.56)$

Therefore,

lower limit : 36.44

upper limit : 39.56