Answer to Question #193279 in Statistics and Probability for Jamaica manzo

Question

State the null hypothesis and the alternative hypothesis in (a) words and (b) symbols for the following

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 of the test, μ= 50 with σ= 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.)We have given that,

$n = 200$

$\bar x = 62$

$s = 5$

$\mu = 50$

$\sigma = 10$

Null hypothesis

$H_0 : \mu = 50$

Alternative hypothesis,

$H_1 : \mu \ne 50$

$z value = \dfrac{\bar x - \mu}{10} = \dfrac{62-50}{10} = 1.2$

At 0.05 level of significance z = 1.96

Hence, calculated value of z score is less than 1.96.

Null hypothesis is verified.