Question

The following are the samples of lifetimes (in hours) of AA size batteries from two different brands:

Brand I = [238, 247, 249, 247, 242, 244, 247, 247, 249,
244, 239, 242, 247, 248, 254, 245, 246, 244,
243, 248, 246, 244, 241, 245, 243, 250, 249,
241, 250, 243, 246, 250, 241, 246, 240, 237,
249, 245, 242, 239]

Brand II = [245, 243, 234, 240, 242, 237, 241, 240, 240,
239, 242, 245, 236, 244, 241, 242, 235, 241,
246, 236, 232, 233, 241, 250, 244, 247, 240,
246, 239, 242, 239, 238, 241, 238, 245, 241,
242, 239, 245, 237, 243, 239, 236, 238, 237,
239, 239, 241, 242, 239]

a. Calculate the sample means, medians of both brands.
b. Calculate the sample variances of both the samples.
c. Give a two sided 97% confidence interval for μ1.For the following parts, assume that the populations follow normal distributions.
d. Give a two sided 90% confidence interval for σ^2_1/σ^2_2
e. Give a one sided upper 97% confidence interval for μ1−μ2.
Do "Brand I" batteries have longer lifetime?
f. Suppose a pack of six batteries from "Brand I" costs $8, and the same size pack from "Brand II" costs $6.
Which brand costs less in terms of energy cost per hour?

Answer 1

Dear student, we can provide you with 4 subquestion answer at a time, please repost for the rest.

a) Brand I:

Mean = 244.925

The median is the middle number in a sorted list of numbers. So, to find the median, we need to place the numbers in value order and find the middle number.

Ordering the data from least to greatest, we get:

237   238   239   239   240   241   241   241   242   242   242   243   243   243   244   244   244   244   245   245   245   246   246   246   246   247   247   247   247   247   248   248   249   249   249   249   250   250   250   254   

As you can see, we do not have just one middle number but we have a pair of middle numbers, so the median is the average of these two numbers:

Median=

Brand II:

Mean = 240.42

The median is the middle number in a sorted list of numbers. So, to find the median, we need to place the numbers in value order and find the middle number.

Ordering the data from least to greatest, we get:

232   233   234   235   236   236   236   237   237   237   238   238   238   239   239   239   239   239   239   239   239   240   240   240   240   241   241   241   241   241   241   241   242   242   242   242   242   242   243   243   244   244   245   245   245   245   246   246   247   250   

As you can see, we do not have just one middle number but we have a pair of middle numbers, so the median is the average of these two numbers:

b)

Brand I :

Brand II:

c) confidence interval for mean is

for 97% confidence and df= n-1= 40-1=39

d) Now we have to compute the confidence interval for the ratio of variance

the degree of freedom 1 :

the degree of freedom 2:

for