We consider the problem of improving lithium car batteries. A research group is makıng great advances using a new type anode and they claim that the mean life is greater than 1600 recharge cycles. To support this claim, they create 36 new batteries and subject them to recharge cycles until they fail. The claim will be established if the sample mean lifetime is greater than 1640 cycles. Otherwise, the claim will not be established and further improvements are needed. Assume that the population standard deviation o = 192 cycles is known. (a) Find the probability of a Type I error. (b) Find the probability of a Type II error when µ = 1680 cycles.

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We consider the problem of improving lithium car batteries. A research group is
makıng great advances using a new type anode and they claim that the mean life is greater
than 1600 recharge cycles. To support this claim, they create 36 new batteries and subject
them to recharge cycles until they fail. The claim will be established if the sample mean
lifetime is greater than 1640 cycles. Otherwise, the claim will not be established and further
improvements are needed. Assume that the population standard deviation o = 192 cycles
is known.
(a)
Find the probability of a Type I error.
(b)
Find the probability of a Type II error when u = 1680 cycles.
Transcribed Image Text:We consider the problem of improving lithium car batteries. A research group is makıng great advances using a new type anode and they claim that the mean life is greater than 1600 recharge cycles. To support this claim, they create 36 new batteries and subject them to recharge cycles until they fail. The claim will be established if the sample mean lifetime is greater than 1640 cycles. Otherwise, the claim will not be established and further improvements are needed. Assume that the population standard deviation o = 192 cycles is known. (a) Find the probability of a Type I error. (b) Find the probability of a Type II error when u = 1680 cycles.
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