Prepare a written response to the following questions.

Chapters 9 &11

1.      Two boats, the Prada (Italy) and the Oracle (USA), are competing for a spot in the upcoming America’s Cup race. They race over a part of the course several times. The sample times in minutes for the Prada were: 12.9, 12.5, 11.0, 13.3, 11.2, 11.4, 11.6, 12.3, 14.2, and 11.3.  The sample times in minutes for the Oracle were: 14.1, 14.1, 14.2, 17.4, 15.8, 16.7, 16.1, 13.3, 13.4, 13.6, 10.8, and 19.0. For data analysis, the appropriate test is the t-Test: Two-Sample Assuming Unequal Variances.

The next table shows the results of this independent t-test. At the .05 significance level, can we conclude that there is a difference in their mean times? Explain these results to a person who knows about the test for a single sample but is unfamiliar with the test for independent means.

Hypothesis Test: Independent Groups (t-test, unequal variance)
        
 PradaOracle     
 12.17014.875mean    
 1.0562.208std. dev.    
 1012n    
        
  16df    
  -2.7050difference (Prada – Oracle)  
  0.7196standard error of difference  
  0hypothesized difference  
        
  -3.76 t    
  .0017 p-value (two-tailed)   
        
  -4.2304confidence interval 95.% lower  
  -1.1796confidence interval 95.% upper  
  1.5254margin of error   
        

2.      The Willow Run Outlet Mall has two Haggar Outlet Stores, one located on Peach Street and the other on Plum Street. The two stores are laid out differently, but both store managers claim their layout maximizes the amounts customers will purchase on impulse. A sample of ten customers at the Peach Street store revealed they spent the following amounts more than planned: $17.58, $19.73, $12.61, $17.79, $16.22, $15.82, $15.40, $15.86, $11.82, $15.85. A sample of fourteen customers at the Plum Street store revealed they spent the following amounts more than they planned when they entered the store: $18.19, $20.22, $17.38, $17.96, $23.92, $15.87, $16.47, $15.96, $16.79, $16.74, $21.40, $20.57, $19.79, $14.83. For Data Analysis, a t-Test: Two-Sample Assuming Unequal Variances was used.

At the .01 significance level is there a difference in the mean amount purchased on an impulse at the two stores?Explain these results to a person who knows about the test for a single sample but is unfamiliar with the test for independent means.

Hypothesis Test: Independent Groups (t-test, unequal variance)
       
 Peach StreetPlum Street    
 15.868018.2921mean   
 2.33062.5527std. dev.   
 1014n   
       
  20df   
  -2.42414difference (Peach Street – Plum Street)
  1.00431standard error of difference 
  0hypothesized difference 
       
  -2.41 t   
  .0255 p-value (two-tailed)  
       
  -5.28173confidence interval 99.% lower 
  0.43345confidence interval 99.% upper 
  2.85759  margin of error  
       

3.      Fry Brothers heating and Air Conditioning, Inc. employs Larry Clark and George Murnen to make service calls to repair furnaces and air conditioning units in homes. Tom Fry, the owner, would like to know whether there is a difference in the mean number of service calls they make per day. Assume the population standard deviation for Larry Clark is 1.05 calls per day and 1.23 calls per day for George Murnen. A random sample of 40 days last year showed that Larry Clark made an average of 4.77 calls per day. For a sample of 50 days George Murnen made an average of 5.02 calls per day. At the .05 significance level, is there a difference in the mean number of calls per day between the two employees? What is the p-value?

Hypothesis Test: Independent Groups (t-test, pooled variance)
        
 LarryGeorge     
 4.775.02mean    
 1.051.23std. dev.    
 4050n    
        
  88 df    
  -0.25000difference (Larry – George)  
  1.33102pooled variance   
  1.15370pooled std. dev.   
  0.24474standard error of difference  
  0hypothesized difference  
        
  -1.02 t    
  .3098 p-value (two-tailed)   
        
  -0.73636confidence interval 95.% lower  
  0.23636confidence interval 95.% upper  
  0.48636  margin of error   

Chapters 11 & 12

4.      A consumer organization wants to know if there is a difference in the price of a particular toy at three different types of stores. The price of the toy was checked in a sample of five discount toy stores, five variety stores, and five department stores. The results are shown below.

Discount toyVarietyDepartment
$121519
131717
141416
121820
151719

An ANOVA was run and the results are shown below.  At the .05 significance level, is there a difference in the mean prices between the three stores? What is the p-value?  Explain why an ANOVA was used to analyze this problem.

One factor ANOVA    
       
 MeannStd. Dev  
 13.251.30Discount Toys  
 16.251.64Variety  
 18.251.64Department  
 15.9152.56Total  
       
ANOVA table      
SourceSS   dfMSF   p-value 
Treatment63.33231.66713.38.0009 
Error28.40122.367   
Total91.7314    

5.      A physician who specializes in weight control has three different diets she recommends. As an experiment, she randomly selected 15 patients and then assigned 5 to each diet. After three weeks the following weight losses, in pounds, were noted. At the .05 significance level, can she conclude that there is a difference in the mean amount of weight loss among the three diets?

Plan APlan BPlan C
567
778
479
558
469

An ANOVA was run and the results are shown below.  At the .01 significance level, is there a difference in the weight loss between the three plans? What is the p-value?  What can you do to determine exactly where the difference is?

One factor ANOVA    
       
 MeannStd. Dev  
 5.051.22Plan A  
 6.250.84Plan B  
 8.250.84Plan C  
 6.5151.64Total  
       
ANOVA table      
SourceSS  dfMSF   p-value 
Treatment26.13213.06713.52.0008 
Error11.60120.967   
Total37.7314    
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