An electronics company has developed a newbattery design that is expected to have a mean life of1,200cycles (H

0

:=1200

).To test this, a single sample of6batteries is taken.We can further assume thatbattery life is normally distributed, and from the 6 samples we determine a sample standard deviation ofS

= 38 cycles and sample mean ofx

= 1224 cycles.

For all questions assume a significance level of

= 0.05

(Q.1)

Given this hypothesis, what is the p-value of this sample?

(Q.2)

If we consider the sample mean and sample standard deviation as the true mean and SD, what would be the resulting new p-value?

(Q.3)

The marketing department at the company wants to advertise this new battery with as high a lifetime as possible, but they don't want too many batteries to die after fewer cycles than the advertised lifetime. If marketing is willing to have 10% of batteries die in fewer cycles than the advertised lifetime, what should the claimed lifetime be, based on the sample of 6 batteries? Round to the nearest cycle (i.e., round to the nearest integer, don't report any decimal places)