Question

A set of solar batteries is used in a research satellite. The satellite can run on only one battery, but it runs best if more than one battery is used. The variance σ² 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. Why? If the variance is too large, the batteries are simply not dependable. Why? Engineers have determined that a variance of σ² = 23 months (squared) is most desirable for these batteries. A random sample of 24 batteries gave a sample variance of 15.2 months (squared). Using a 0.05 level of significance, test the claim that σ² = 23 against the claim that σ² is different from 23.

1)Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.)

2)What are the degrees of freedom?

3) Find a 90% confidence interval for the population variance. (Round your answers to two decimal places.)

4)Find a 90% confidence interval for the population standard deviation. (Round your answers to two decimal places.)

Answer 1

Give : Sample size=n=24

Sample variance=

Specified value of the population variance =

Significnace level=

Hypothesis : Vs

1) The test statistic is ,

2 ) The degrees of freedom = n-1 = 24-1 = 23

Critical value :

Decision : Here , From Excel "=CHIINV(0.025,23)"

Therefore , fail to reject Ho at 0.05 significance level.

Conclusion : Hence , the population variance is 23.

3) The 90% confidence interval for the population variance is ,

4) The 90% confidence interval for the population standard deviation is ,