PSY315

Week 4 Practice Worksheet

 

Prepare a written response to the following questions.

 

Chapters 9 &11

 

    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 t test for a single sample but is unfamiliar with the t test for independent means.

 
Hypothesis Test: Independent Groups (t-test, unequal variance)
                            
    Prada     Oracle                     
    12.170     14.875     mean                 
    1.056     2.208     std. dev.                 
    10     12     n                 
                            
        16     df                 
        -2.7050     difference (Prada – Oracle)         
        0.7196     standard error of difference         
        0     hypothesized difference         
                            
        -3.76      t                 
        .0017      p-value (two-tailed)             
                            
        -4.2304     confidence interval 95.% lower         
        -1.1796     confidence interval 95.% upper         
        1.5254     margin of error             
                           

    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 t test for a single sample but is unfamiliar with the t test for independent means.

 
Hypothesis Test: Independent Groups (t-test, unequal variance)
                        
    Peach Street     Plum Street                 
    15.8680     18.2921     mean             
    2.3306     2.5527     std. dev.             
    10     14     n             
                        
        20     df             
        -2.42414     difference (Peach Street – Plum Street)
        1.00431     standard error of difference     
        0     hypothesized difference     
                        
        -2.41      t             
        .0255      p-value (two-tailed)         
                        
        -5.28173     confidence interval 99.% lower     
        0.43345     confidence interval 99.% upper     
        2.85759       margin of error         
                        

 

    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)
                            
    Larry     George                     
    4.77     5.02     mean                 
    1.05     1.23     std. dev.                 
    40     50     n                 
                            
        88     df                 
        -0.25000     difference (Larry – George)         
        1.33102     pooled variance             
        1.15370     pooled std. dev.             
        0.24474     standard error of difference         
        0     hypothesized difference         
                            
        -1.02      t                 
        .3098      p-value (two-tailed)             
                            
        -0.73636     confidence interval 95.% lower         
        0.23636     confidence interval 95.% upper         
        0.48636       margin of error             

 

Chapters 11 & 12

 

    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 toy     Variety     Department
$12     15     19
13     17     17
14     14     16
12     18     20
15     17     19

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                 
                        
      Mean     n     Std. Dev               
    13.2     5     1.30     Discount Toys         
    16.2     5     1.64     Variety         
    18.2     5     1.64     Department         
      15.9     15     2.56     Total         
                          
ANOVA table                           
Source     SS        df     MS     F        p-value     
Treatment     63.33     2     31.667     13.38     .0009     
Error     28.40     12     2.367             
Total     91.73     14                       

 

    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 A     Plan B     Plan C
5     6     7
7     7     8
4     7     9
5     5     8
4     6     9

 

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                 
                        
      Mean     n     Std. Dev               
    5.0     5     1.22     Plan A         
    6.2     5     0.84     Plan B         
    8.2     5     0.84     Plan C         
      6.5     15     1.64     Total         
                          
ANOVA table                           
Source     SS        df     MS     F        p-value     
Treatment     26.13     2     13.067     13.52     .0008     
Error     11.60     12     0.967             
Total     37.73     14