Question

In: Statistics and Probability

The manufacturer of a certain brand of auto batteries claims that the mean life of these...

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 24 such batteries and found that the mean life for this sample is 43.15 months. The lives of all such batteries have a normal distribution with the population standard deviation of 4.5 months.

Find the p-value for the test of hypothesis with the alternative hypothesis that the mean life of these batteries is less than 45 months.

Round your answer to four decimal places.

p=

Solutions

Expert Solution

solution:

this is the left tailed test .  

The null and alternative hypothesis is ,

H0 :   = 45

Ha : < 45

Test statistic = z

= ( - ) / / n

= (43.15-45) / 4.5/ 24

z = -2.01

P(z < -2.01 ) = 0.0222 uisng z table

P-value = 0.0222


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