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Hypothesis Testing for One-way ANOVA
Related Topics
Wize University Statistics Textbook > Analysis of Variance
Hypothesis Testing for One-Way ANOVA
3 Activities
You wish to compare the hourly sales of 5 fast-food restaurants to see if they are different. Here is the summarized data:
Write the appropriate Ho and Ha
H
0
:
μ
1
=
μ
2
=
μ
3
=
μ
4
=
μ
5
H_0:\ \mu_1=\mu_2=\mu_3=\mu_4=\mu_5
H
0
:
μ
1
=
μ
2
=
μ
3
=
μ
4
=
μ
5
H
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H_1:\ the\ means\ are\ all\ different\ from\ each\ other
H
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:
t
h
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an
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H
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μ
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H_0:\ \mu_1=\mu_2=\mu_3
H
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μ
1
=
μ
2
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μ
3
H
1
:
a
t
l
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H_1:\ at\ least\ one\ of\ the\ \mu\ is\ different\ from\ the\ others
H
1
:
a
t
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a
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μ
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H
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H_0:\ at\ least\ one\ of\ the\ \mu\ is\ different\ from\ the\ others
H
0
:
a
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H
1
:
μ
1
=
μ
2
=
μ
3
=
μ
4
=
μ
5
H_1:\ \mu_1=\mu_2=\mu_3=\mu_4=\mu_5
H
1
:
μ
1
=
μ
2
=
μ
3
=
μ
4
=
μ
5
H
0
:
μ
1
=
μ
2
=
μ
3
=
μ
4
=
μ
5
H_0:\ \mu_1=\mu_2=\mu_3=\mu_4=\mu_5
H
0
:
μ
1
=
μ
2
=
μ
3
=
μ
4
=
μ
5
H
1
:
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H_1:\ at\ least\ one\ of\ the\ \mu\ is\ different\ from\ the\ others
H
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More Hypothesis Testing for One-Way ANOVA Questions:
Hypothesis Testing: One Way Anova
A math teacher would like to know whether or not different teaching methods have an effect on his students’ marks. He randomly samples 12 students and teaches one-third of them the traditional blackboard note-taking method, one-third are instructed to learn with their peers as a group, and the remaining 4 are told to read his notes online. After one week he decides to give them a quiz to see if there are differences in the mean quiz scores.
Here are the results:
Hypothesis Testing: One-way ANOVA
You wish to compare the hourly sales of 5 fast-food restaurants to see if they are different. Here is the summarized data:
Given that the p-value of the test-statistic is 0.11, the appropriate conclusion at the 10% level of significance is
Hypothesis Testing for One-way ANOVA
The Real Housewives of Beverly Hills, Orange County, Atlanta, and New York are arguing in a limo about which city charges the most for nose jobs.
Which of the following can be stated as the hypotheses:
Hypothesis Testing: One-way ANOVA
A study was conducted to analyze the average decrease in blood pressure in patients with stage 2 hypertension. 5 different medications were tested, each medication being tested on 7 patients. The ANOVA F-test was used to test for any difference in mean decreases in the blood pressures across the 5 medications. What is the distribution of the test statistic under the null hypothesis?
Hypothesis Testing: One-way ANOVA
You wish to compare the hourly sales of 5 fast-food restaurants to see if they are different. Here is the summarized data:
Write the appropriate Ho and Ha
Hypothesis Testing: One-way ANOVA
There are four candidates running for President of Panem. It is suspected that some candidates are favoured over others based on who got the most speaking time during the debates. The average airtime for each candidate based on the last several debates is summarized here:
Given that the sum of squares of the treatments (between) is 1 354.125 and the sum of squares of the errors (within) 298.83333,
a) What is the value of the test-statistic? Round to 3 decimal places
Hypothesis testing: one-way ANOVA
The Real Housewives of Beverly Hills, Orange County, Atlanta, and New York are arguing in a limo about which city charges the most for nose jobs.
Using a p-value of 0.04093, the appropriate conclusion at the 5% level of significance is
Hypothesis Testing: One-way ANOVA
The Real Housewives of Beverly Hills, Orange County, Atlanta, and New York are arguing in a limo about which city charges the most for nose jobs.
Which of the following can be stated as the hypotheses:
Hypothesis Testing: One-way ANOVA
The London Transit Commission would like to know if ridership varies by bus routes. Four routes with low ridership are sampled in 7 random days of the month.
Some of the results are listed below in the anova table:
Compute the F-statistic.
Hypothesis testing: One-way ANOVA
You wish to compare the hourly sales of 5 fast-food restaurants to see if they are different. Here is the summarized data:
Given that the p-value of the test-statistic is 0.11, the appropriate conclusion at the 10% level of significance is
Hypothesis Testing: One-way ANOVA
The London Transit Commission would like to know if ridership varies by bus routes. Four routes with low ridership are sampled in 7 random days of the month.
Some of the results are listed below in the anova table:
What are the degrees of freedom of the F-statistic?
Hypothesis Testing: One Way Anova
A math teacher would like to know whether or not different teaching methods have an effect on his students’ marks. He randomly samples 12 students and teaches one-third of them the traditional blackboard note-taking method, one-third are instructed to learn with their peers as a group, and the remaining 4 are told to read his notes online. After one week he decides to give them a quiz to see if there are differences in the mean quiz scores.
Here are the results:
Hypothesis Testing: One-way ANOVA
Which of the following is
not
a correct alternative hypothesis for an analysis of variance F-test?
Hypothesis Testing: One-way ANOVA
A bookstore wants to know if the mean sales are the same across 4 genres, which are action and adventure, crime, horror, and drama. Here is a limited anova table:
If the p-value is 0.048, what is your conclusion at alpha = 5% ?
Hypothesis Testing for One-way ANOVA
A math teacher would like to know whether or not different teaching methods have an effect on his students’ marks. He randomly samples 12 students and teaches one-third of them the traditional blackboard note-taking method, one-third are instructed to learn with their peers as a group, and the remaining 4 are told to read his notes online. After one week he decides to give them a quiz to see if there are differences in the mean quiz scores.
Here are the results:
a) State the null and alternative hypothesis.
Confidence interval and Hypothesis testing
Mr. Emin loves going to Starbucks drive-thru on his busy mornings but he can’t help feeling frustrated by the amount of time he has to wait to be served. He decides to go to Starbucks for 5 days and Tim Hortons for 7 days. He records the length of time, rounded to the nearest minute he has to wait each day to be served. Here is the data
The standard deviation for Starbucks waiting time is 3.082.
The standard deviation for Tim Hortons waiting time is 2.160.
Hypothesis Testing for One-way ANOVA
We want to compare the typing speed of paralegals on different laptops. We sample 5 paralegals, and have them type on 4 different laptops, recording the number of words per minute they type. The results are shown below:
Conduct a Block Design test at the 5% significance level. The ANOVA results are below:
Hypothesis Testing: One-way ANOVA
5 new pills are tested with the aim of reducing blood pressure.
4 participants are assigned to each pill and their blood pressure is measured.
Here is some of the data:
Hypothesis Testing: One-way ANOVA
Dr. Anova is teaching several sections of his statistics courses. His midterm averages haven't been great this year. He asks you to help him decide if the means of the classes are different.
a) How many classes does he teach?
b) How many students does he have?
Hypothesis Testing: One-way ANOVA
The Real Housewives of Beverly Hills, Orange County, Atlanta, and New York are arguing in a limo about which city charges the most for nose jobs.
Using the results from Question 3, if
α
=
0.01
\alpha=0.01
α
=
0.01
select the correct conclusion from the following:
Hypothesis testing for one-way ANOVA
The English Premiere League and the Spanish Liga record the number of goals opportunities for several games. The league administrators want to determine whether the variance of goals opportunities in the two leagues are equal at the 5% significance level.
n
1
=
11
a
n
d
n
2
=
15
n_1=11\ and\ n_2=15
n
1
=
11
an
d
n
2
=
15
s
1
=
7.21
a
n
d
s
2
=
8.32
s_1=7.21\ and\ s_2=8.32
s
1
=
7.21
an
d
s
2
=
8.32
