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To test H0: ? = 100 versus H1:? ? 100, a simple random
Chapter 6, Problem 5AYU(choose chapter or problem)
Problem 5AYU
To test H0: μ = 100 versus H1:μ ≠ 100, a simple random sample of size n = 23 is obtained from a population that is known to be normally distributed.
(a) If = 104.8 and 5 = 9.2, compute the test statistic.
(b) If the researcher decides to test this hypothesis at the α = 0.01 level of significance, determine the critical values.
(c) Draw a t-distribution that depicts the critical region.
(d) Will the researcher reject the null hypothesis? Why?
(e) Construct a 99% confidence interval to test the hypothesis.
Questions & Answers
QUESTION:
Problem 5AYU
To test H0: μ = 100 versus H1:μ ≠ 100, a simple random sample of size n = 23 is obtained from a population that is known to be normally distributed.
(a) If = 104.8 and 5 = 9.2, compute the test statistic.
(b) If the researcher decides to test this hypothesis at the α = 0.01 level of significance, determine the critical values.
(c) Draw a t-distribution that depicts the critical region.
(d) Will the researcher reject the null hypothesis? Why?
(e) Construct a 99% confidence interval to test the hypothesis.
ANSWER:
Answer :
Step 1
a)
Here the hypothesis H0: μ = 100 versus H1:μ ≠ 100, a simple random sample of size n = 23 is obtained from a population that is known to be normally distributed.
We know that
= 104.8, s=9.2,
= 100 and n = 23.
The formula of the test statistic is
t =
t =
t =
t =
t = 2.502
Hence the test statistic 2.502