Connexions

You are here: Home » Content » Collaborative Statistics » Practice 2: Single Mean, Unknown Population Standard Deviation

Lenses

What is a lens?

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags?

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

In these lenses

• Exercises

This module is included inLens: Mihai Nica's Lens
By: Mihai Nica

Click the "Exercises" link to see all content selected in this lens.

Recently Viewed

This feature requires Javascript to be enabled.

Tags

(What is a tag?)

These tags come from the endorsement, affiliation, and other lenses that include this content.

Inside Collection (Textbook):

Textbook by: Barbara Illowsky, Ph.D., Susan Dean. E-mail the authors

Practice 2: Single Mean, Unknown Population Standard Deviation

Summary: This module provides a practice of Hypothesis Testing of Single Mean and Single Proportion as a part of Collaborative Statistics collection (col10522) by Barbara Illowsky and Susan Dean.

Student Learning Outcomes

• The student will conduct a hypothesis test of a single mean with unknown population standard deviation.

Given

A random survey of 75 death row inmates revealed that the mean length of time on death row is 17.4 years with a standard deviation of 6.3 years. Conduct a hypothesis test to determine if the population mean time on death row could likely be 15 years.

Hypothesis Testing: Single Mean

Exercise 1

Is this a test of means or proportions?

averages

Exercise 2

State the null and alternative hypotheses.

• a. Ho:Ho: size 12{H rSub { size 8{O} } :} {}
• b. Ha:Ha: size 12{H rSub { size 8{a} } :} {}

Solution

• a. H o : μ = 15 H o : μ = 15 size 12{H rSub { size 8{O} } :μ="15"} {}
• b. H a : μ 15 H a : μ 15 size 12{H rSub { size 8{a} } :μ <> "15"} {}

Exercise 3

Is this a right-tailed, left-tailed, or two-tailed test? How do you know?

two-tailed

Exercise 4

What symbol represents the Random Variable for this test?

Solution

X ¯ X ¯ size 12{ {overline {X}} } {}

Exercise 5

In words, define the Random Variable for this test.

Solution

the mean time spent on death row for the 75 inmates

Exercise 6

Is the population standard deviation known and, if so, what is it?

No

Exercise 7

Calculate the following:

• a. x¯=x¯= size 12{ {overline {x}} ={}} {}
• b. 6.3=6.3= size 12{6 "." 3={}} {}
• c. n=n= size 12{n={}} {}

Solution

• a. 17.4
• b. ss size 12{s} {}
• c. 75

Exercise 8

Which test should be used? In 1 -2 complete sentences, explain why.

Solution

tt size 12{t - {}} {}test

Exercise 9

State the distribution to use for the hypothesis test.

Solution

t 74 t 74 size 12{t rSub { size 8{"74"} } } {}

Exercise 10

Sketch a graph of the situation. Label the horizontal axis. Mark the hypothesized mean and the sample mean, x¯x¯ size 12{ {overline {x}} } {}. Shade the area corresponding to the p-value.

Exercise 11

Find the p-value.

0.0015

Exercise 12

At a pre-conceived α=0.05α=0.05 size 12{α=0 "." "05"} {}, what is your:

• a. Decision:
• b. Reason for the decision:
• c. Conclusion (write out in a complete sentence):

Solution

• a. Reject the null hypothesis

Discussion Question

Does it appear that the mean time on death row could be 15 years? Why or why not?

Content actions

PDF | EPUB (?)

What is an EPUB file?

EPUB is an electronic book format that can be read on a variety of mobile devices.

Collection to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags?

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks

Module to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags?

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks