LINK TO TEXT Part 2 The manufacturer of a certain brand of auto batteries claims

Question

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Part 2

The manufacturer of a certain brand of auto batteries claims that the mean life of these batteries is 50 months. A consumer protection agency that wants to check this claim took a random sample of 23 such batteries and found that the mean life for this sample is 47.83 months. The lives of all such batteries have a normal distribution with the population standard deviation of 4.5 months. Will you reject the manufacturer's claim at a significance level of 0.025 with alternative hypothesis that the mean life of these batteries is less than 50 months?


(a) Identify H0:

You answered correctly! Move on to the next part to add to your understanding of this problem. m = 50m < 50

(Use m instead of )

Identify H1:

You answered correctly! Move on to the next part to add to your understanding of this problem. m < 50m = 50

(Use m instead of )


(b) Identify

You answered correctly! Move on to the next part to add to your understanding of this problem.

months


(c) Identify .


=

You answered correctly! Move on to the next part to add to your understanding of this problem.

months

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Attempts: 3 of 5 used

Explanation / Answer

Part 1:
a) H0: The mean life of these batteries is 50 months
mu = 50
H1: The mean life of these batteries is less than 50 months
mu < 50

b)Xbar = 47.83
c) Sigma = SD = s = 4.5

Part 2:

a) Standard error = S/sqrt(n) = 4.5/sqrt(23)= 0.9383

b) Test statistic z = (xbar - mu) / SE = (47.83-50)/0.9383 = -2.3127
c) Z-crtical value = -2.0739
d)
P-Value: 0.0152

since P-value < alpha 0.025, so we reject H0
Thus we conclude that
The mean life of these batteries is less than 50 months
mu < 50

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