In: Statistics and Probability
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=
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