Question

State the null hypothesis and the alternative hypothesis in (a) words and in 

(b) symbols for each of the following.

a. A random sample of 200 students got a mean score of 62 with a standard deviation score of 5

in a knowledge test in mathematics. In the standardization, = 50 with = 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

$\bar x = 62$

$s = 5$

$\mu = 50$

$\sigma = 10$

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 $= 1.96$

Hence calculated z score is less than the 1.96. Therefore null hypothesis is verified.