Question

The average marks in the mathematics of a sample of 100 students was 51 with a S.D. of 6 marks .Could this have been a random sample from the population with average marks 50.

Answer 1

Solution:

Here $n=100, \bar{x}=51, s=6, \mu=50$ ; $\sigma$ is unknown.

$\mathrm{H}_{0}$ : The sample is drawn from a population with mean $50, \mu=50$

$\mathrm{H}_{1}: \mu \neq 50$

Under $\mathrm{H}_{0}, z=\frac{\bar{x}-\mu}{s / \sqrt{n}}=\frac{51-50}{6 / \sqrt{100}}=\frac{10}{6}=1.6666$ .

Conclusion. Since $|z|=1.666<1.96, z_{\alpha}$ the significant value of z at 5% level of significance, $\mathrm{H}_{0}$ is accepted, i.e., the sample is drawn from the population with mean 50 .