Question

A random sample of n = 45 values give = 63. Can this sample be regarded as drawn from a

A normal population with mean μ = 70 and s2 =25?

Answer 1

Hypothesis

$H_0:\bar x =70$

$H_1:\bar x \not=70$

Since sample size $45 >30$ we use the normal distribution table

$$Z= \frac{\bar x - \mu}{\sqrt{s^2}}$$

$\bar x= 63$

$\mu=70$

$s^2= 25$

Therefore

$$Z= \frac{63 - 70}{\sqrt{25}}= -1.4$$

At a $95\%$ level of confidence, the sample mean can be concluded to be equal to the population mean $\mu =70$ if:

$$-1.96<Z<1.96$$

Since the Z value obtained is within the range i.e.

$$-1.96<-1.4<1.96$$

We conclude that the sample is from the normal population with mean = 70 and variance = 25