Question 339300
· State the null and alternate hypotheses
Ho: {{{sigma=3}}}
Ha: {{{sigma<3}}}
---
· Calculate the sample standard deviation
{{{s=3.335}}}
--
· Determine which test statistic is appropriate (chi-square or F), and calculate its value.
test statistic:  {{{(n-1)*S^2/(sigma[0])^2=(15-1)*3.335^2/3^2=17.30}}}
--
· Determine the critical value(s).
lower tail 
Chi^2 (1-alpha, dof)=chi^2(0.99,14)=4.66
---
· State your decision: Should the null hypothesis be rejected? 
since test statistic=17.30>critical value=4.66 cannot reject Ho.
Conclusion:  No evidence against {{{sigma=3}}}