Aresearch engineer for a tire manufacturer is investigating tire life for a new rubber compound. she has built 10 tires and tested them to end-of-life in a road test. the sample mean and standard deviation are 61,492 and 2990 kilometers, respectively. assume population is approximately normally distributed. (a) can you conclude, using =0.05, that the standard deviation of tire life exceeds 3000 km ? yes ot no ?
The standard deviation of tire life does exceed 3000 km
This is a Chi-Square Hypothesis Test for the Standard Deviation, here we have
so, this is an upper one-tailed test.
The test statistic is
n = 10 is the sample size
s = sample standard deviation
= population standard deviation
we would reject the null hypothesis if
is the critical value corresponding to the level of significance with n-1 degrees of freedom.
we can use either a table or a spreadsheet to compute this value.
In Excel use
In OpenOffice Calc use
and we get this value equals 3.3251
Working out our T statistic
Since T > 3.3251 we reject the null and conclude that the standard deviation of tire life exceeds 3000 km.
what statement? is there an image?
the answer is 21%.