amaraea
05.09.2019 •
Mathematics
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.
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Ответ:
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).
Ответ:
A-15=55
is the correct equations.