Exercise 15. For the following four cases, perform statistical tests with significance level a = 5%, testing the hypothesis Ho: = 0 against the alternative H₁:0. Show how you perform each test and state the outcome. a) We have observed 100 independent, normally distributed values with known variance o2 = 1. The average of the observed values is -0.18. b) We have observed 10 independent samples of a normal distribution with known variance ²4: The observed values are 0.595, 3.923, 0.12, 1.078, 0.578, 1.575, 2.26, -0.031, 1.733, and 1.135. c) We have observed 10 independent samples from a normal distribution. The sample mean is = -1.405, the exact variance is unknown but the sample variance is s² = 1.456.

Exercise 15. For the following four cases, perform statistical tests with significance level a = 5%, testing the hypothesis Ho: = 0 against the alternative H₁:0. Show how you perform each test and state the outcome. a) We have observed 100 independent, normally distributed values with known variance o2 = 1. The average of the observed values is -0.18. b) We have observed 10 independent samples of a normal distribution with known variance ²4: The observed values are 0.595, 3.923, 0.12, 1.078, 0.578, 1.575, 2.26, -0.031, 1.733, and 1.135. c) We have observed 10 independent samples from a normal distribution. The sample mean is = -1.405, the exact variance is unknown but the sample variance is s² = 1.456.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

file：http://www1.maths.leeds.ac.uk/~arief/MATH1712/docs/ex07-q21d.csv

Exercise 15. For the following four cases, perform statistical tests with significance level a = 5%,
testing the hypothesis Ho: μ = 0 against the alternative H₁: 0. Show how you perform each
test and state the outcome.
a) We have observed 100 independent, normally distributed values with known variance o² = 1.
The average of the observed values is -0.18.
b) We have observed 10 independent samples of a normal distribution with known variance
o² = 4: The observed values are 0.595, 3.923, 0.12, 1.078, 0.578, 1.575, 2.26, -0.031, 1.733,
and 1.135.
c) We have observed 10 independent samples from a normal distribution. The sample mean is
= -1.405, the exact variance is unknown but the sample variance is s² = 1.456.
d) We have observed the independent samples given in the file
http://www1.maths.leeds.ac.uk/~arief/MATH1712/docs/ex07-q21d.csv
Hint: be careful when importing this csv file into R.

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