Question

Suppose a group is interested in determining whether teenagers obtain their drivers licenses at approximately the same average age across the country. Suppose that the following data are randomly collected from four teenagers in each region of the country. The numbers represent the age at which teenagers obtained their drivers licenses. Northeast South West Central East 16.3 16.9 16.4 16.2 17.1 16.1 16.5 16.5 16.6 17.2 16.4 16.4 16.6 16.5 16.6 16.5 16.2 16.1 16.4 16.8 Using your preferred technique (e.g., by hand, Excel, online software, etc.), answer the following questions. Do we need to conduct a multiple comparison of means for this problem? If so, which pairs of means test differently using either the Bonferroni correction or the two-sample t-test assuming unequal variances. If we don’t need to do any further testing, state simply why not.

          Suppose a group is interested in determining whether teenagers
obtain their drivers licenses at approximately the same average age
across the country. Suppose that the following data are randomly
collected from four teenagers in each region of the country.
 The numbers represent the age at which teenagers obtained
their drivers licenses.
           
Northeast        
South              
West               
Central            
East
           
16.3                 
16.9                 
16.4                 
16.2                 
17.1
           
16.1                 
16.5                 
16.5                 
16.6                 
17.2
           
16.4                 
16.4                 
16.6                 
16.5                 
16.6
           
16.5                 
16.2                 
16.1                 
16.4                 
16.8
                       
           
Using your preferred technique (e.g., by hand, Excel, online
software, etc.), answer the following questions.
Do we need to conduct a multiple comparison of means for this
problem?  If so, which
           
pairs of means test differently using either the Bonferroni
correction or the two-sample t-test assuming unequal
variances.  If we don’t need to do any further testing, state
simply why not.

Show more…

Added by Brandi S.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Madhur L

03/03/2023

Step 1

Null hypothesis (H0): The average age at which teenagers obtain their driver's licenses is the same across all regions. Alternative hypothesis (H1): The average age at which teenagers obtain their driver's licenses is not the same across all regions. Show more…

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Suppose a group is interested in determining whether teenagers obtain their drivers licenses at approximately the same average age across the country. Suppose that the following data are randomly collected from four teenagers in each region of the country. The numbers represent the age at which teenagers obtained their drivers licenses. Northeast South West Central East 16.3 16.9 16.4 16.2 17.1 16.1 16.5 16.5 16.6 17.2 16.4 16.4 16.6 16.5 16.6 16.5 16.2 16.1 16.4 16.8 Using your preferred technique (e.g., by hand, Excel, online software, etc.), answer the following questions. Do we need to conduct a multiple comparison of means for this problem? If so, which pairs of means test differently using either the Bonferroni correction or the two-sample t-test assuming unequal variances. If we don’t need to do any further testing, state simply why not.

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Transcript

00:01 Hello students, let us do this question.

00:03 Here we have given data of age of teenagers when they get driving lessons for the five regions.

00:10 The regions are north east, south, west, central and east region.

00:26 And we have to compare if the means for the five regions is same or not.

00:30 So we will use here one factor an hour.

00:33 The hypothesis to be tested here is mean for all regions is same.

00:37 So mu1 equal to mu 2 equal to mu 3 equal to mu 4 equal to mu 5, which have nothing but the population mean for these 5 regions respectively.

00:49 Alternative hypothesis here will be mu i not equal to mu j, where i comma j goes from 1 to 3, 4, 5.

01:00 I is not equal to j for at least one fair of i and j.

01:04 It means either we can have mu1 not equal to mu two or mute in mu two not equal to mu three or so on for taking various combinations of five comma j where i is not equal to j the excel steps to perform the one one factor anvice first enter data into five columns then select data go to data analysis after that no one window will open from then select and 1 factor for input range select the complete input data range alpha equal to 0 .05 if labors are selected while selecting the input then click labels equal to yes and for output range click on any blank cell and click okay then you will get the anva output the ano output the second table is nothing but the actual ano output where it contains the value of the ms degrees of freedom ss p value and f critical so from this test we can see our f test statistic value is 2 .4757...

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