# Help me to solve this Hypothesis problem

• Jun 22nd 2007, 02:18 PM
Help me to solve this Hypothesis problem
Past experience indicates that the time for high school seniors to complete standardized test is a normal random variable with a standard deviation of 6 minutes. Test the hypothesis that sigma=6 against the alternative that sigma< 6 if a random sample of 20 high school seniors has a standard deviation s=4.51. Use a 0.05 level of significance.
• Jun 22nd 2007, 10:15 PM
CaptainBlack
Quote:

Past experience indicates that the time for high school seniors to complete standardized test is a normal random variable with a standard deviation of 6 minutes. Test the hypothesis that sigma=6 against the alternative that sigma< 6 if a random sample of 20 high school seniors has a standard deviation s=4.51. Use a 0.05 level of significance.

This question requires the use of the variance ratio of F-test. The null hypothesis is thst $\displaystyle \sigma=6$, the 95-th percentile for the
F-distribution with $\displaystyle n_1=\infty$ and $\displaystyle n_2=19$
is $\displaystyle 1.88$,

So:

$\displaystyle F=\frac{6^2}{4.51^2}=1.769<1.88$

So our results fail the lower one-tailled test, so we reject the null hypothesis
in favour of the alternative that $\displaystyle \sigma<6$.