Question

A random sample of 900 members is found to have a mean of 4.45 cms.
Can it be reasonably regarded as a sample from a large population whose
mean is 5 cms and varaince is 4 cms

Answer 1

Null hypothesis $H_0:\mu=5.$

Alternative hypothesis $H_a:\mu\ne5.$

Test statistic: $z=\frac{\bar x-\mu}{\sqrt{\frac{\sigma^2}{n}}}=\frac{4.45-5}{\sqrt{\frac{4}{900}}}=-8.25.$

P-value: $p=2P(Z<-8.25)<0.0001.$

Since the P-value is less than 0.05, reject the null hypothesis.

It cannot be reasonably regarded as a sample from a large population whose

mean is 5 cms and varaince is 4 cms.