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.
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.
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