Question

Please help!!! Must show full written work, thank you!!!!!

Question 7. (One Variance) A set of solar batteries is used in a research satellite. The satellite can only run on one battery, but it runs best if more than one battery is used. The variance σ 2 of lifetimes of these batteries affects the useful lifetime of the satellite before it goes dead. If the variance is too small, all the batteries will tend to die at once. If the variance is too large, the batteries are simply not dependable. Engineers have determined that a variance of σ 2 = 23 months (squared) is most desirable for these batteries. A random sample of 22 batteries gave a sample variance of 14.3 months (squared). Assume the data is normally distributed. Using a 0.05 level of significance, test the claim that σ 2 is different from 23. (10 points)

Answer 1

Ans:

sample size,n=22

sample variance=14.3

Test statistic:

Chi square=(22-1)*14.3/23=13.057

critical chi square values:

CHIINV(0.025,21)=35.479

CHIINV(0.975,21)=10.283

Rejection region: chi square<10.283 or chi square>35.479

As,test statistic does not fall in rejevtion region,we fail to reject H0.

There is not sufficient evidence to conclude that population variance is different from 23.