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A random sample of 20 observations selected from a normal
Chapter 7, Problem 113SE(choose chapter or problem)
Problem 113SE
A random sample of 20 observations selected from a normal population produced = 72.6 and s2 = 19.4.
Questions & Answers
QUESTION:
Problem 113SE
A random sample of 20 observations selected from a normal population produced = 72.6 and s2 = 19.4.
ANSWER:
Answer
Step 1 of 2
(a)
A random sample of observations selected from a normal population produced
Test
Since the sample size is very less, hence we will use the test statistic.
A lower or left tailed test about a population mean is,
Rejection rule for a lower tail test: The Critical Value Approach,
……..(1)
Hence the test statistic for hypothesis tests about a population mean when is known,
………(2)
We know hence we can rewrite the equation (2),
………(3)
The rejection region requires
in the lower tail of the
with
From the table III, Appendix D, the value of
…….(4)
From equation (3) and (4) we can see that the observed value of the test statistic falls in the rejection region.
Since,
Hence is rejected.
There is sufficient evidence to indicate that the mean is less than 80 at