A battery manufacturer hopes to make a new kind of battery that will last reliab

Question

A battery manufacturer hopes to make a new kind of battery that will last reliably longer the average battery (statistically speaking) However because this is a new battery design, there is also a chance that the battery will not last as long as the average battery. You randomly choose 25 batteries from a day's production and run them continuously until they fall. The average run for the sample of 25 batteries is 302.58 hours, with a sample Standard deviation of 5.0 hours. It is known that the average battery lasts for 300.00 hours. The population standard deviation is unknown. A. State the nuIl hypothesis B. State the alternative hypothesis. C. Suppose the population standard deviation for running batteries was known. What test would be appropriate now? D. What would be the new critical value for a = .05 ?

Explanation / Answer

Given

No of batteries = n = 25

Actual mean (u)= 302.58 hrs

Estimated mean (x) = 300 hrs

standard deviation (s) = 5 hrs

a) Null hypothesis : x = u

b) Alternate hypothsis: x is not equal to u

c) If the population standard deviation is known we would have used Z test comparing two populations

If not there, we use single sample Z test comparing only with mean

d) Critical value for a = 0.05 Z level is 1.96 (standard form)

_____________________________________

Z test

= (x-u)/(s/sqrt(n))

= -5.76

is greater than critical Z value

Hence alternate hypothesis is satisfied

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