Expert: Ahmed Salami - 10/26/2008

Question
A telescope manufacturer wants its telescopes to have standard deviation in resolution to be significantly below 2 whan focusimng on object 500 light -year away.when a telescope is used to focus on an object 500 light year away 30 times, the sample standard deviation turns out to be 1.46.
(A)     state explict null and alternate hypotheses.
(B)     test your hypothesis at the  = 0.01 level.

Answer
Hi Akanksha,
I'm sorry but i just noticed some numerical errors in the original solution and i've made corrections. Please forgive any inconvenience.
a) The Null Hypothesis
 H0: S = 2   (S represents standard deviation)
 The Alternative Hypothesis
 H1: S < 2

b) The test a hypothesis about a standard deviation, we use the chi-
 square statistic   
 c^2(pronounced chi-square) = (n-1)s^2/S^2
 where (small case) s is the sample standard deviation
 And so,
 c^2 = (30-1)(1.46)^2/2^2
     = 29(2.1316)/4
     = 15.45

 We use the chi-square distribution with the number of degrees of
 freedom (n-1). The test is one-tailed and to get the critical value
 from the table you need the point with area 0.01 to the left of it.
 From the table, this value is 14.26. And so we see that 15.45 doesnt      
 fall in the rejection zone and we therefore accept the null
 hypothesis.
 Hence, we reject the alternative hypothesis that the standard
 deviation in resolution is significantly below 2 at α = 0.01

Regards.

  Regards.