Answer:
The standard deviation of tire life does exceed 3000 km
Step-by-step explanation:
This is a Chi-Square Hypothesis Test for the Standard Deviation, here we have
[tex] \bf H_0: \sigma = 3000[/tex]
[tex] \bf H_a: \sigma > 3000[/tex]
so, this is an upper one-tailed test.
The test statistic is
[tex]\bf T=\frac{(n-1)s^2}{\sigma^2}[/tex]
where
n = 10 is the sample size
s = sample standard deviation
[tex]\bf \sigma[/tex] = population standard deviation
we would reject the null hypothesis if
[tex]\bf T>\chi^2_{(\alpha,n-1)}[/tex]
where
[tex]\bf \chi^2_{(\alpha,n-1)}[/tex]
is the critical value corresponding to the level of significance [tex]\bf \alpha[/tex] with n-1 degrees of freedom.
we can use either a table or a spreadsheet to compute this value.
In Excel use
CHISQ.INV(0.05,9)
In OpenOffice Calc use
CHISQINV(0.05;9)
and we get this value equals 3.3251
Working out our T statistic
[tex]\bf T=\frac{(n-1)s^2}{\sigma^2}=\frac{9*(2990)^2}{(3000)^2}=8.9401[/tex]
Since T > 3.3251 we reject the null and conclude that the standard deviation of tire life exceeds 3000 km.
