3. A random sample of 30 individuals is obtained from a large
population with a known standard deviation of = 4.6. If
the sample mean is observed to be 17.12, test H0:
> 18 versus the alternative H1:
< 18 using the p-value approach at
the = 0.05 level of significance. What is the p-value
value of the test?
Round your answer to the nearest thousandths.
Answer =
Solution :
This is the left tailed test .
The null and alternative hypothesis is ,
H0 : 18
H1 : 18
Test statistic = z
= ( - ) / / n
= (17.12 - 18) / 4.6 / 30 = -1.048
Test statistic = -1.048
P(z < -1.048) = 0.147
P-value = 0.147
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