Buying a new laptop can be an overwhelming experience, with so many technical features and specifications to consider along battery life. After searching on the Internet, you consider two brands: Apple and Orange.

a)Suppose that you can randomly sample 20 of 100 laptops from an Apple store and find the sample mean battery life is 779 minutes and the standard deviation is 42 minutes. Construct 95% confidence intervals for the true mean of the battery life of Apple laptops.

[7 marks]

b)Suppose that you can also randomly sample 20 of 80 laptops from another store, Orange, and find the sample mean battery life is 812 minutes and the standard deviation is 109 minutes. Construct 95% confidence intervals for the true mean for the battery life of Orange laptops.

[7 marks]

c)Based on the confidence intervals found in part a) and b), what brand should you buy if you think battery life is the most important feature of your laptop? Explain your decision. Are there any points of concern that should be taken into account when you make the decision?