27 test scores in a math class have a standard deviation of 12.3. use a .05 significance level and to test that this class has a standard deviation less than 14.1. state the null and alternative hypotheses, the p-value, and conclusion.

The standard deviation of test scores in the class is not less than 14.1

Step-by-step explanation:

Let's suppose that the test scores follow a normal distribution. Besides, we have:

a) Standard deviation

b) Significance level

c) n=27

Using a) we can deduce that sample variance .

Since we want to prove if the population variance is less than :

(Null hypotesis) :

(Alternative hypotesis):

For test this kind of hypotesis (variance in one population) the correct test statistic is , which under  have Chi-square distribution with n-1 degrees of freedom.

Calculating the test statistic ( is the value in   ) :

For this hypotesis (left one tailed test) the p-value is where M follow a Chi-square distribution with n-1=26 degrees of freedom.You can check in a chi-square table that p-value=0.1986

If then there is no evidence to statistically reject . Therefore, the standard deviation of test scores in the class is not less than 14.1 (95% confidence level).