A psychologist at a private mental hospital was asked to determine whether there was a clear difference in the length of stay for patients with different categories of diagnosis.  Looking at the last four patients in each of the three major categories, the results (in terms of weeks of stay) were as follows: Diagnosis Category Affective DisordersCognitive DisordersDrug-Related Conditions71286810591261110Using alpha = 0.05, is there a significant difference in length of stay among diagnosis categories?  Show all five steps of hypothesis testing and compute the means and standard deviations for each group.

Question
Asked Nov 25, 2019
2 views

A psychologist at a private mental hospital was asked to determine whether there was a clear difference in the length of stay for patients with different categories of diagnosis.  Looking at the last four patients in each of the three major categories, the results (in terms of weeks of stay) were as follows:

 

Diagnosis Category

 

Affective Disorders

Cognitive Disorders

Drug-Related Conditions

7

12

8

6

8

10

5

9

12

6

11

10

Using alpha = 0.05, is there a significant difference in length of stay among diagnosis categories?  Show all five steps of hypothesis testing and compute the means and standard deviations for each group. 

check_circle

Expert Answer

Step 1

Given data

Affective Disorders Cognitive Disorders Drug-Related Conditions
7
12
10
8
5
12
6
11
10
help_outline

Image Transcriptionclose

Affective Disorders Cognitive Disorders Drug-Related Conditions 7 12 10 8 5 12 6 11 10

fullscreen
Step 2

Formulation of hypothesis

Null Hypothesis is :- There is no difference in the length of stay for patients with different categories of diagnosis. 

 H0: µAffective Disorders = µCognitive Disorders = µDrug-Related Conditions

Alternative Hypothesis is :- There is significant difference in the length of stay for patients with different categories of diagnosis. 

 

Hα: µAffective Disorders ≠ µCognitive Disorders ≠ µDrug-Related Conditions

Steps to perform ANOVA in Excel is given below

  • Enter the data in Excel
  • GO to data->data analysis->select Anova: Single Factor
  • Enter the following data in this table
X
Anova: Single Factor
Input
OK
Input Range:
SAS1:SCS5
Cancel
Grouped By:
Columns
O Rows
Help
Labels in first row
Alpha: 0.05
Output options
Output Range:
SIS8:SSS30
New Worksheet Ply:
O New Workbook
help_outline

Image Transcriptionclose

X Anova: Single Factor Input OK Input Range: SAS1:SCS5 Cancel Grouped By: Columns O Rows Help Labels in first row Alpha: 0.05 Output options Output Range: SIS8:SSS30 New Worksheet Ply: O New Workbook

fullscreen
Step 3

Result obtained f...

Anova: Single Factor
SUMMARY
Groups
Count
Sum
Average Variance
Affective Disorders
24
6 0.66667
Cognitive Disorders
Drug-Related Conditic
40
10 3.33333
4
40
10 2.66667
ANOVA
F crit
Source of Variation
df
P-value
SS
MS
F
Between Groups
2 21.3333
42.6667
9.6 0.00586 4.25649
Within Groups
20
9 2.22222
Total
62.6667
11
help_outline

Image Transcriptionclose

Anova: Single Factor SUMMARY Groups Count Sum Average Variance Affective Disorders 24 6 0.66667 Cognitive Disorders Drug-Related Conditic 40 10 3.33333 4 40 10 2.66667 ANOVA F crit Source of Variation df P-value SS MS F Between Groups 2 21.3333 42.6667 9.6 0.00586 4.25649 Within Groups 20 9 2.22222 Total 62.6667 11

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Math

Statistics

Related Statistics Q&A

Find answers to questions asked by student like you

Show more Q&A add
question_answer

Q: .

A: It is given that 800 out of 1,000 students use Facebook during class.The sample proportion is 800/1,...

question_answer

Q: In a survey, 20 people were asked how much they spent on their child's last birthday gift. The resul...

A: IntroductionThe 100 (1 – α) % confidence interval for the population mean, μ, for given sample stand...

question_answer

Q: Test whether mu 1 less than mu 2μ1<μ2 at the alphaαequals=0.01 level of significance for the samp...

A: To calculate the p value, we need the data and the data provided by you is incompleteSo, using the p...

question_answer

Q: Please help me with this problem

A: The test hypotheses are given below:Null hypothesis:H0:p=0.11Alternative hypothesis: Ha:p≠0.11The va...

question_answer

Q: For each of the following sample proportions and sample sizes,  compute a 99% confidence interval fo...

A: It is given that n =25 and sample proportion = 0.40.Since the required confidence interval is 99%, t...

question_answer

Q: a socialogist expects the life expenancy of people in africa is different than the life expantancy o...

A: From the provided information, the following values are given as:

question_answer

Q: when comparing the means of samples from two normally distributed populations, if the samples are in...

A: Conditions for using z-test is,The samples are randomly selected.The samples are independent.Sample ...

question_answer

Q: Observation 1 2 3 4 5 6 7 8 di negative 1.8−1.8 negative 0.7−0.7 negativ...

A: The required values are obtained as follows:

question_answer

Q: 7

A: Lack of memory property:Let the random variable X is exponentially distributed with parameter 1/λ. I...