Understanding Basic Statistics 6th Edition by Charles Henry Brase,Corrinne Pellillo Brase

Exercise 28

For Problems 3-11, please provide the following information:
(a) What is the level of significance State the null and alternate hypotheses.
(b) Find the value of the chi-square statistic for the sample. What are the degrees of freedom Check Requirements What assumptions are you making about the original distribution
(c) Find or estimate the P -value of the sample test statistic.
(d) Based on your answers in parts (a)-(c), will you reject or fail to reject the null hypothesis of independence
(e) Interpret your conclusion in the context of the application.
In each of the following problems, assume a normal population distribution.
Engineering: Solar Batteries 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 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. Why If the variance is too large, the batteries are simply not dependable. Why Engineers have determined that a variance of 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). Using a 0.05 level of significance, test the claim that 2 = 23 against the claim that 2 is different from 23.