Question

the mean life of a name brand aa battery is 19 hours. a consumer group is interested in determining if generic aa batteries have a shorter mean life. this group tested a random sample of 9 generic AA batteries resulting in a mean life of 17.4 hours with a standard deviation of 1.5 hours. you may assume that battery lives follow a normal distribution. At 1% level of significance, do the generic AA batteries have a mean life shorter than 19 hours?

Answer 1

This is the left tailed test .

The null and alternative hypothesis is

H₀ : = 19

H_a : < 19

Test statistic = t

= ( - ) / s / n

= (17.4 - 19) / 1.5 / 9

= -3.2

Test statistic = -3.2

df = 8

P-value = 0.0063

= 0.01

P-value <

Reject the null hypothesis .

There is sufficient evidence to conclude that the generic AA batteries have a mean life shorter than 19 hours