Question

1. A manufacturer claims that its rechargeable batteries are good for an average 1,000 charges with a standard deviation of 25 charges. A random sample of 20 batteries has a mean life of 992 charges. Perform an appropriate hypothesis test with α = 0.05, assuming the distribution of the number of recharges is approximately normal. Hypothesis:

Test statistic:

p-value:

Conclusion:

Interpretation:

Answer 1

Solution :

= 1000

=992

S =25

n = 20

This is the two tailed test .

The null and alternative hypothesis is ,

H0 :    = 1000

Ha :     1000

Test statistic = t

= ( - ) / S / n

= (992-1000) /25 / 20

= −1.431

Test statistic = t =  −1.431

P-value =0.1686

= 0.05  

P-value >

0.1686 > 0.05

Fail to reject the null hypothesis .

There is not sufficient evidence to claim that the population mean μ is different than 1000, at the 0.05 significance level