MATH 215|Mathematics 215 Introduction to Statistics
Assignment 4 scored 85 out of 92 2025 Athabasca Universit
Assignment 4
good work on a difficult unit!
Overview
Total marks: / 92
This assignment covers content from Unit 4 of the course. It assesses your knowledge of sampling
distributions that refer to probability distributions of sample statistics, such as the sample mean and sample
proportion, and your ability to use sampling distributions in estimation and in hypothesis testing about
population means and population proportions.
Instructions
• Show all your work and justify all of your answers and conclusions, except for the True/False
questions.
• Keep your work to 4 decimals, unless otherwise stated.
• Note: Finishing a test of hypotheses with a statement like “reject H0” or “do not reject H0” will be
insufficient for full marks. You must also provide a written concluding statement in the context of the
problem itself. For example, if you are testing hypotheses about the effectiveness of a medical
treatment, you must conclude with a statement like, “we can conclude that the treatment is effective” or
“we cannot conclude that the treatment is effective.”
(9 total marks)
1. The duration of long-distance telephone calls is normally distributed with a mean of µ = 18 minutes
and a standard deviation of = 12 minutes. If a random sample of 64 telephone calls is used to reflect
on the population of all long-distance calls, what is the probability that the sample mean call duration:
(3 marks)
a. will be more than 14 minutes?
(6 marks)
b. will be either less than 15 minutes or more than 20.5 minutes?
Mathematics 215: Introduction to Statistics Assignment 4 1
, Mathematics 215: Introduction to Statistics Assignment 4 2
Assignment 4 scored 85 out of 92 2025 Athabasca Universit
Assignment 4
good work on a difficult unit!
Overview
Total marks: / 92
This assignment covers content from Unit 4 of the course. It assesses your knowledge of sampling
distributions that refer to probability distributions of sample statistics, such as the sample mean and sample
proportion, and your ability to use sampling distributions in estimation and in hypothesis testing about
population means and population proportions.
Instructions
• Show all your work and justify all of your answers and conclusions, except for the True/False
questions.
• Keep your work to 4 decimals, unless otherwise stated.
• Note: Finishing a test of hypotheses with a statement like “reject H0” or “do not reject H0” will be
insufficient for full marks. You must also provide a written concluding statement in the context of the
problem itself. For example, if you are testing hypotheses about the effectiveness of a medical
treatment, you must conclude with a statement like, “we can conclude that the treatment is effective” or
“we cannot conclude that the treatment is effective.”
(9 total marks)
1. The duration of long-distance telephone calls is normally distributed with a mean of µ = 18 minutes
and a standard deviation of = 12 minutes. If a random sample of 64 telephone calls is used to reflect
on the population of all long-distance calls, what is the probability that the sample mean call duration:
(3 marks)
a. will be more than 14 minutes?
(6 marks)
b. will be either less than 15 minutes or more than 20.5 minutes?
Mathematics 215: Introduction to Statistics Assignment 4 1
, Mathematics 215: Introduction to Statistics Assignment 4 2
