Question

A sample of 900 members is found to have a mean of 3.47 cm. can it be reasonably regarded as a simple sample from a large population with mean 3.23 cm. and standard deviation 2.31 cm ?

Answer 1

I think answerer #1 missed the point of the question. This is really a hypothesis test question. Is it reasonable to assume mu=3.23 if x-bar=3.47? The answer is "no". The hypothesis test yields a p-value of 9.1393764*10^(-4) or about 1/1094. This means there is a 1/1094 chance of getting an x-bar that extreme (3.47) if the actual mean is 3.23. It is unreasonable to expect a 1/1094 chance happening randomly; consequently, you assume that (actually) mu>3.23.

Answer 2

A sample of 900 members is found to have a mean of 3.47 cm.

Upon taking the null hypothesis that the mean of samples is equal to 3.23 cm, we can write,

H0 : μH₀ = 3.23

Ha : μH₀ = 3.23

From given, we have,

$\bar{X}$ = 3.47 cm

σp = 2.31 cm

n = 900

The test statistics z can be given as,

$z=\dfrac{\bar{X}-\mu_{H_{0}}}{\frac {\sigma_p} {\sqrt n}}$

$z=\dfrac{3.47 - 3.23}{\frac {2.31} {\sqrt {900}}}$

z = 0.24 / 0.077

z = 3.11

As, 3.11 is an acceptable region, so the simple sample from a large population with mean 3.23 cm. and standard deviation 2.31 cm is reasonable.