Respuesta :
Answer:
The number of degrees of freedom for this hypothesis test is 14.
Step-by-step explanation:
In this case the professor wants to determine whether the average number of minutes that a student needs to complete a statistics exam has a standard deviation that is less than 5.0 minutes.
Then the variance will be, [tex]\sigma^{2}=(5.0)^{2}=25[/tex]
The hypothesis to determine whether the population variance is less than 25.0 minutes or not, is:
H₀: The population variance is not less than 25.0 minutes, i.e. σ² = 25.
Hₐ: The population variance is less than 25.0 minutes, i.e. σ² < 25.
The test statistics is:
[tex]\chi ^{2}_{cal.}=\frac{ns^{2}}{\sigma^{2}}[/tex]
The decision rule is:
If the calculated value of the test statistic is less than the critical value, [tex]\chi^{2}_{(1-\alpha), (n-1)}[/tex] then the null hypothesis will be rejected.
Here,
α = level of significance
(n - 1) = degrees of freedom
The degrees of freedom is the number of values that can change throughout a statistical hypothesis test.
Compute the degrees of freedom as follows:
[tex]df=n-1=15-1=14[/tex]
Thus, the number of degrees of freedom for this hypothesis test is 14.
