Stat Assignment Set

1) What is the critical F value for a sample of 7 observations in the numerator and 6 in the denominator? Use a two-tailed test and the 0.1 significance level. (Round your answer to 2 decimal places.)

  F  

2) Arbitron Media Research Inc. conducted a study of the iPod listening habits of men and women. One facet of the study involved the mean listening time. It was discovered that the mean listening time for men was 29 minutes per day. The standard deviation of the sample of the 10 men studied was 8 minutes per day. The mean listening time for the 12 women studied was also 29 minutes, but the standard deviation of the sample was 15 minutes. At the .10 significance level, can we conclude that there is a difference in the variation in the listening times for men and women? (Round your answer to 3 decimal places.)

  The test statistic is  . Decision   

3) The following is sample information. Test the hypothesis that the treatment means are equal. Use the 0.01 significance level.

Treatment 1 Treatment 2 Treatment 3
7           4           4         
4           5           7         
6           5           6         
6           4           5         
________________________________________

(a) State the null hypothesis and the alternate hypothesis.

 
  H0 

  H1 

________________________________________

(b) What is the decision rule? (Round your answer to 2 decimal places.)

    H0 if the test statistic is greater than  .

(c&d) Compute SST, SSE, and SS total and complete an ANOVA table. (Round SS, MS and F values to 3 decimal places.)

  Source SS df MS F
  Treatments     
  
  
  

  Error   
  
  
 
  ________________________________________ ________________________________________   
  Total   
  
  
  ________________________________________________________________________________ ________________________________________________________________________________   
________________________________________

(e) State your decision regarding the null hypothesis.
   
   H0

4) A senior accounting major at Midsouth State University has job offers from four CPA firms. To explore the offers further, she asked a sample of recent trainees how many months each worked for the firm before receiving a raise in salary. The sample information is submitted to MINITAB with the following results:

  Analysis of Variance        
  Source DF SS MS F
  Factor 5        36.39    7.28    1.92   
  Error 12        45.54    3.80     
  Total 17        81.93          
________________________________________

Reject if F >  . (Round your answer to 2 decimal places.)

At the 0.01 level of significance, is there a difference in the mean number of months before a raise was granted among the four CPA firms? 

5) The following data are given for a two-factor ANOVA.

   Treatment
  ________________________________________
Block 1 2
A 43 36
B 37 23
C 42 37
________________________________________

Using the .05 significance level conduct a test of hypothesis to determine whether the block or the treatment means differ.

(a) State the null and alternate hypotheses for treatments;

  
  H0 

  H1 

________________________________________

(b) State the decision rule for treatments. (Round your answer to 1 decimal place.)

    H0 if the test statistic is greater than  .

(c) State the null and alternate hypotheses for blocks.

  
  H0 

  H1 

________________________________________

Also, state the decision rule for blocks.

 if the test statistic is greater than  .

(d&e) Compute SST, SSB, SS total, and SSE and complete an ANOVA table. (Round SS, MS and F values to 2 decimal places.)

  Source SS df MS F
  Treatments     
    
    
    

  Blocks     
    
    
    

  Error     
    
    
 
  ________________________________________ ________________________________________   
  Total     
    
  
  ________________________________________________________________________________ ________________________________________________________________________________   
________________________________________

(f) Give your decision regarding the two sets of hypotheses.

 
  Decision: Treatments.  

  Decision: Blocks. 

6) Chapin Manufacturing Company operates 24 hours a day, five days a week. The workers rotate shifts each week. Management is interested in whether there is a difference in the number of units produced when the employees work on various shifts. A sample of five workers is selected and their output recorded on each shift. At the 0.01 significance level, can we conclude there is a difference in the mean production rate by shift or by employee?

  Units Produced
  ________________________________________
  Employee Day Afternoon Night
  Skaff 35 22 31
  Lum 36 26 34
  Clark 23 27 35
  Treece 32 21 27
  Morgan 21 24 24
________________________________________

For treatments: Reject Ho if F >  . (Round your answer to 2 decimal places.)

For blocks: Reject Ho if F>  . (Round your answer to 2 decimal places.)

Decision by shift:  difference in the mean production rate.

Decision by employee:  difference in the mean production rate.

7) A study of the effect of television commercials on 12-year-old children measured their attention span, in seconds. The commercials were for clothes, food, and toys.

Clothes Food Toys
27 44 61
22 49 64
46 37 57
35 56 48
28 47 63
31 42 53
17 34 48
31 43 58
20 57 47
  47 51
  44 51
  54 
________________________________________

(1) Complete the ANOVA table. Use .05 significance level. (Round the SS and MS values to 1 decimal place and F value to 2 decimal places. Leave no cells blank - be certain to enter "0" wherever required.)

  Source DF SS MS F P
  Factors    
   
   
   
   

  Error    
   
   
  
  ________________________________________ ________________________________________     
  Total    
   
    
  ________________________________________________________________________________ ________________________________________________________________________________     
________________________________________

(2) Find the values of mean and standard deviation. (Round the mean and standard deviation values to 3 decimal places.)

  Level N Mean StDev
  Clothes    
   
   

  Food    
   
   

  Toys    
   
   

________________________________________

(3) Is there a difference in the mean attention span of the children for the various commercials?

  The hypothesis of identical means can definitely be .

  There is  in the mean attention span.

(4) Are there significant differences between pairs of means?

  Clothes have a mean attention span of at least ten minutes  the other groups.

8) When only two treatments are involved, ANOVA and the Student t test (Chapter 11) result in the same conclusions. Also, . As an example, suppose that 14 randomly selected students were divided into two groups, one consisting of 6 students and the other of 8. One group was taught using a combination of lecture and programmed instruction, the other using a combination of lecture and television. At the end of the course, each group was given a 50-item test. The following is a list of the number correct for each of the two groups. Using analysis of variance techniques, test the null hypothesis, that the two mean test scores are equal.

Lecture and
Programmed
Instruction Lecture and
Television
14 33
12 21
26 34
25 20
16 29
14 28
  21
  22
________________________________________

(a-1) Complete the ANOVA table. (Round SS, MS and F values to 2 decimal places.)

  Source SS df MS F
  Factors    
   
   
   

  Error    
   
   
 
  ________________________________________ ________________________________________   
  Total    
   
  
  ________________________________________________________________________________ ________________________________________________________________________________   
________________________________________

(a-2) Use a level of significance. (Round your answer to 2 decimal places.)

  The test statistic is F   

(b) Using the t test from Chapter 11, compute t. (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.)

  t   

(c) There is  in the mean test scores.

9) The city of Tucson, Arizona, employs people to assess the value of homes for the purpose of establishing real estate tax. The city manager sends each assessor to the same five homes and then compares the results. The information is given below, in thousands of dollars. Can we conclude that there is a difference in the assessors, at α = 0.05?

Assessor
________________________________________
Home Zawodny Norman Cingle Holiday
A $53 $55 $48 $43
B   50   54   54   56
C   45   58   42   57
D   76   63   61   61
E   83   81   93   85
________________________________________

(a) Is there a difference in the treatment means, at α = .05? (Round your answer to 2 decimal places.)

The computed F value is  .

Decision:  a difference in the treatment means.

(b) Is there a difference in the block means, at α = .05? (Round your answer to 2 decimal places.)

The computed F is  .

Decision:  a difference in the block means.

10) Three supermarket chains in the Denver area each claim to have the lowest overall prices. As part of an investigative study on supermarket advertising, the Denver Daily News conducted a study. First, a random sample of nine grocery items was selected. Next, the price of each selected item was checked at each of the three chains on the same day. Use 0.01 level of significance.

Item Super$ Ralph's Lowblaws
1 $2.30 $1.23 $1.24
2 2.30 1.70 1.78
3 2.40 3.20 3.10
4 2.40 1.78 1.87
5 1.32 1.47 1.32
6 4.01 3.06 1.82
7 4.31 3.53 2.21
8 4.13 3.07 2.35
9 5.02 4.17 4.21
________________________________________
 
 

(a-9) Is there a difference in the item means and in the store means?

  There is  in the item means. There is  in the store means.