Question

5. A company in the AAA alkaline battery manufacturing industry wants to ensure a given weight for the batteries they put on the market. To do this, they randomly select 35 batteries and record the weight (in grams) of each battery. Let µ be the mean weight for the population of the batteries produced by this company. Suppose that the resulting 95% confidence interval is (11.45, 11.69).

(a) Consider the following statement: There is a 95% chance that µ is between 11.45 and 11.69. Is this statement correct? Why or why not?

(b) Consider the following statement: We can be highly confident that 95% of all batteries produced by this company weigh between 11.45 and 11.69. Is this statement correct? Why or why not?

(c) Consider the following statement: If the procedure of selecting a sample of size 50 and then computing the corresponding 95% interval is repeated 100 times, 95 of the resulting intervals will include µ. Is this statement correct? Why or why not?

(d) Assuming that the population standard deviation is = 0.54, how large a sample is required to estimate the mean weight for the population of the batteries produced by this company within 0.05 grams with 95% confidence?

Answer 1

(a) The statement is correct .

As (11.45 , 11.69) is the 95% confidence interval for population mean , we can say that there is 95% chance that is between 11.45 and 11.69 .

(b) The statement is wrong  

As (11.45 , 11.69) is the 95% confidence interval for population mean , that is this interval is the interval estimate of ,we can estimate the interval within which is expected to contain , we cannot estimate about the entire population.  .

(c) The statement is correct .

As (11.45 , 11.69) is the 95% confidence interval for population mean , thus if we construct confidence interval for samples of same size , 95% of them is expected to contain the population mean   .

(d) Given

margin of error =0.05

For 95% confidence , zc = 1.96

( rounding to integer)

Required sample size =448

(d)