Question

3. A manufacturer of photographic flash batteries took a sample of 13 batteries from the production of any given day and used them continuously until they were used up. Battery life in hours until it ran out was: 342, 426, 317, 545, 264, 451, 749, 631, 512, 266, 492, 562 and 298. With a significance level of 0.05, there is evidence that the Battery life is more than 400 hours? (assume that life times have normal distribution)

Answer 1

3. For the given data

Create the following table.

data	data-mean	(data - mean)2
342	-108.3846	11747.22151716
426	-24.3846	594.60871716
317	-133.3846	17791.45151716
545	94.6154	8952.07391716
264	-186.3846	34739.21911716
451	0.61540000000002	0.37871716000003
749	298.6154	89171.15711716
631	180.6154	32621.92271716
512	61.6154	3796.45751716
266	-184.3846	33997.68071716
492	41.6154	1731.84151716
562	111.6154	12457.99751716
298	-152.3846	23221.06631716

Find the sum of numbers in the last column to get.

So

Now we need test the claim that mean>400

So hypothesis is vs

As sample size is less than 30 and also population standard deviation is not known, we will use t statistics

So

P value is TDIST(1.21,12,1)=0.1248>alpha=0.05

Hence we fail to reject the null hypothesis

Hence we do not have sufficient evidence to support the claim that mean is greater than 400 hours.