Answer to Question #209329 in Statistics and Probability for Jhay

Question

Write the null hypothesis in words and in symbols.

1. A random sample of 200 students got a mean score of 62 with s-5 in a knowledge test in Mathematics. In the standardization of the test, -50 with o-10.

Answer 1

a.) The null hypothesis is a typical statistical theory which suggests that no statistical relationship and significance exists in a set of given single observed variable, between two sets of observed data and measured phenomena.

b.)

$$n= 200$$

$$s=5$$

$$\mu=50$$

$$\sigma=10$$

Using the null hypothesis,

$H_0 : \mu = 50$

$H_1 : \mu \ne 50$

Value of $z$ can be calculated as $z = \dfrac{\bar x - \mu }{10} = \dfrac{62-50}{10} = 1.2$

At 0.05 level of significance $z_c= 1.96$.

Hence calculated $|z|=1.2<1.96=z_c.$ Therefore null hypothesis is not rejected.

Therefore, there is enough evidence to claim that the population mean $\mu$ is different than 50, at the $\alpha=0.05$  significance level.