SOLUTION: please help me answer these questions; Do the hypothesis testing to answer this question. The manufacturer of a certain brand of auto batteries claims that the mean life of t

Question 1102723: please help me answer these questions;
Do the hypothesis testing to answer this question.
The manufacturer of a certain brand of auto batteries claims that the mean life of these batteries is 45 months. A consumer protection agency that wants to check this claim took a random sample of 36 such batteries and found that the mean life for this sample is 43.75 months with a standard deviation of 4 months. Using 2.5% significance level, would you conclude that the mean life of these batteries is less than 45 months?
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
Null hypothesis, Ho: mean life = 45 months
Alternative hypothesis, Ha: mean life is < 45 months
:
the significance level is the p-value = 0.025 for this problem
:
the standard error of the sample mean is 4/square root(36) = 2/3 approximately 0.67
:
since our sample size is > 30, we will use the normal distribution
:
z-value = (43.75 - 45) / 0.67 = −1.8657
:
the calculated p-value for this z-value is 0.0307
:
since the calculated p-value is > 0.025, we accept the null hypothesis
:
****************************************************************
we conclude that the mean life of the batteries is 45 months
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