Question

Ubercharge advertises that its rechargeable batteries can be recharged over 100 times without any decrease in performance (i.e., reduced battery life). An independent firm purchased 50 Ubercharge batteries and recorded the number of times each battery could be recharged until there was a decrease in performance. They reported an average of 96 recharges before a decrease in battery performance with a standard deviation of 3. Which analysis is appropriate for determining whether Ubercharge's claims should be rejected? Assume that all statistical assumptions are met.

Answer 1

The appropriate test that should be done here is Z-test for the mean, sigma unknown.

So the test is

HO: : = 100 H: < 100

And test statistic is

X - Z II o ſa = sample mean = population mean population standard deviation =sample size n

Hence from the information given,

Sample mean is 96

Population mean is 100

Sigma is 3

and n = 50

We test the hypothesis at 95% confidence level,

Z Test of Hypothesis for the Mean
Data
Null Hypothesis                       m=	100
Level of Significance	0.05
Population Standard Deviation	3
Sample Size	50
Sample Mean	96
Intermediate Calculations
Standard Error of the Mean	0.4243
Z Test Statistic	-9.4281
Lower-Tail Test
Lower Critical Value	-1.6449
p-Value	<.01
Reject the null hypothesis

We reject the null hypothesis at 95% confidence level because -9.42<-1.64.