e. Find the power of the test. f. If µ=1,050 instead of 1,030, what is the probability that the test will incorrectly fail to reject H,? That is, what is B? g. If µ=1,050 instead of 1,030, what is the probability that the test will correctly reject the null hypothesis? That is, what is the power of the test?

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.3: Special Probability Density Functions
Problem 8E
icon
Related questions
icon
Concept explainers
Question

only part E, F, G & H.

6.Suppose you want to test H,: µ=1,000 against Ha: µ>1,000 using a=.025. The population in question
is normally distributed with standard deviation 120. A random sample of size n=36 will be used.
a. Sketch the sampling distribution of i assuming that H, is true.
b. Find the value of *o, that value of i above which the null hypothesis will be rejected. Indicate the
rejection region on your graph of part a. Shade the area above the rejection region and label it a.
c. On your graph of part a, sketch the sampling distribution of i if µ=1,030. Shade the area under this
distribution that corresponds to the probability that i falls in the nonrejection region when
u=1,030, Label this area B.
d. Find B.
e. Find the power of the test.
f. If u=1,050 instead of 1,030, what is the probability that the test will incorrectly fail to reject H,?
That is, what is ß?
g. If u=1,050 instead of 1,030, what is the probability that the test will correctly reject the null
hypothesis? That is, what is the power of the test?
h. What do you learn?
i. If If u=1,050 and n=100, what is the probability that the test will incorrectly fail to reject H,? That
is, what is B?
j. What do you learn from comparing answers for parts f and į?
k. If If u=1,050 and n=100 and a=.01, what is the probability that the test will incorrectly fail to
reject H,? That is, what is ß?
1. What do you learn from comparing answers for parts į and k?
Transcribed Image Text:6.Suppose you want to test H,: µ=1,000 against Ha: µ>1,000 using a=.025. The population in question is normally distributed with standard deviation 120. A random sample of size n=36 will be used. a. Sketch the sampling distribution of i assuming that H, is true. b. Find the value of *o, that value of i above which the null hypothesis will be rejected. Indicate the rejection region on your graph of part a. Shade the area above the rejection region and label it a. c. On your graph of part a, sketch the sampling distribution of i if µ=1,030. Shade the area under this distribution that corresponds to the probability that i falls in the nonrejection region when u=1,030, Label this area B. d. Find B. e. Find the power of the test. f. If u=1,050 instead of 1,030, what is the probability that the test will incorrectly fail to reject H,? That is, what is ß? g. If u=1,050 instead of 1,030, what is the probability that the test will correctly reject the null hypothesis? That is, what is the power of the test? h. What do you learn? i. If If u=1,050 and n=100, what is the probability that the test will incorrectly fail to reject H,? That is, what is B? j. What do you learn from comparing answers for parts f and į? k. If If u=1,050 and n=100 and a=.01, what is the probability that the test will incorrectly fail to reject H,? That is, what is ß? 1. What do you learn from comparing answers for parts į and k?
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps

Blurred answer
Knowledge Booster
Points, Lines and Planes
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Calculus For The Life Sciences
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,