Answer to Question #344764 in Statistics and Probability for Salauddin

Question

The mean height of random sample of 100 individuals from a population is 160 cms. The

S.D. of the sample is 10cms. Would it be reasonable to suppose that the mean height of the

population is 165cms?

Answer 1

Given that $n=100, \=x=160, \sigma=10, \mu=165$

$H_0:\mu=165$ (there is no difference between sample mean and opulation mean)

$H_a: \mu\not=165$ (two-tailed alternative)

The test statistic is given by

$z=\frac{\=x-\mu}{\sigma/\sqrt{n}}\\=\frac{160-165}{10/\sqrt{100}}=-5$

At 5% significance level the tabulated value for $z_{\alpha}=1.96$

|Calculated value|$\le$ Tabulated value then Accept $H_0$

$|5|>1.96$ So we reject $H_0$

That is there is a significant difference between the sample mean and population means.