Durabatt claims to use a superior technology which gives their batteries longer

Question

Durabatt claims to use a superior technology which gives their batteries longer life than, say, Eversteady batteries. Suppose that you purchase 1000 batteries from each company. The sample mean and sample standard deviation of the Durabatt battery lifetimes were determined to be 10.04 and 0.987 hours, respectively, while the sample mean and sample standard deviation of the Eversteady battery lifetimes were 8.972 and 1.032 hours, respectively.

(a) Construct a 95% confidence interval for the mean Durabatt lifetime. State any required assumptions and how you would check these assumptions.

(b) How many samples should you have taken in order to estimate the mean Durabatt lifetime to within 15 minutes with 95% confidence. If an approximation is used, comment on the validity of the approximation.

(c) Would Durabatts claim be reasonable? Substantiate your conclusion with calculations based on a 95% confidence level.

Explanation / Answer

a) mean = 10.04 , std.deviation = 0.987 , n =1000

z value at 95% confidence interval = 1.96

CI = mean + /- z * (s / sqrt(n))

= 10.04 + /- 1.96 * ( 0.987/sqrt(1000))

= (9.989 , 10.101)

b) ME = z *(s/sqrt(n))

15 = 1.96 * ( 0.987 / sqrt(n))

n = 0.0167 = 1.67

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