Hypothesis Testing With Two Samples

profileResearch-Expert
 (Not rated)
 (Not rated)
Chat

 

The production department of the newspaper wants to ensure that the mean blackness of the print for all newspapers is at least 0.97 on a standard scale in which the target value is 1.0.  A random sample of 50 newspapers was selected, and the blackness of on spot of each of the 50 newspapers measured.  Calculate the sample statistics and determine whether there is evidence that the population mean blackness is less than 0.97.

 

 

        

 

 

Blackness

   

 

 

0.854

0.993

1.052

0.898

0.934

   

 

 

1.023

0.762

0.678

0.621

1.06

   

 

 

1.005

0.814

1.162

0.818

1.047

   

 

 

1.03

1.108

0.808

1.113

0.8

   

 

 

1.219

0.805

1.012

1.286

0.889

   

 

 

0.977

1.223

0.859

1.091

1.012

   

 

 

1.044

1.024

0.951

1.086

0.695

   

 

 

0.778

0.884

1.112

1.141

0.869

   

 

 

1.122

0.799

1.003

0.931

0.734

   

 

 

1.114

0.87

0.972

0.723

1.131

   

 

 

The marketing department team was charged with improving the telemarketing process in order to increase the number of home-delivery subscriptions sold.  It is known that the longer a caller speaks to a respondent, the greater the chance that the caller will sell a home-delivery subscription.  Therefore, the team decided to find ways to increase the length of the call.  The team investigated the impact that the time of a call might have on the length.  The team selected a sample of 30 female callers and randomly assigned 15 of to the “early” time period (5-7pm) and 15 to the “later” (7-9pm) time period. The callers knew that the team was observing their efforts that evening but didn’t know which particular calls were monitored.  Measurements were taken on the length of call (defined as the difference, in seconds, between the time the person answers the phone and the time she hangs up).  A. Analyze the data and compare the two independent groups of callers.  B. Suppose that instead of the research design described, there were only 15 callers sampled and each caller was to be monitored twice in the evening – once in the early time period and once in the later time period.  Thus, each of the pairs of values represents a particular caller’s two measurements.  Re-analyzed the data.  How does it compare to part A.

 

 

        

 

 

 

Early

Late

     

 

 

 

41.3

37.1

     

 

 

 

37.5

38.9

     

 

 

 

39.3

42.2

     

 

 

 

37.4

45.7

     

 

 

 

33.6

42.4

     

 

 

 

38.5

39

     

 

 

 

32.6

40.9

     

 

 

 

37.3

40.5

     

 

 

 

40.6

40.7

     

 

 

 

33.3

38

     

 

 

 

39.6

43.6

     

 

 

 

35.7

43.8

     

 

 

 

31.3

34.9

     

 

 

 

36.8

35.7

     

 

 

 

36.3

47.4

     

 

 

In studying the home delivery solicitation process, the marketing department team determined that the so-called “later” calls made between 7pm and 9pm were significantly more conducive to lengthier calls than those made earlier in the evening (between 5-7pm).  The team sought to investigate the effect of the type of presentation on the length of the call.  A group of 24 female callers was randomly assigned, 8 each, to one of three presentation plans – structured, semi-structured, and unstructured – and trained to make the telephone presentation.  All calls were made between 7-9pm and the callers were to provide an introductory greeting that was personal but informal (“Hi, this is Leigh Richardson from the XYZ Times.  May I speak to John Smith?”).  The callers knew that the team was observing their efforts that evening but didn’t know which particular calls were monitored.  Measurements were taken on the length of call (defined as the difference, in seconds, between the time the person answers the phone and the time he or she hangs up).  Analyze the data and compare the three independent groups of callers.

 

 

        

 

 

 

Presentation Plan

    

 

 

 

Structured

Semi-structured

Unstructured

    

 

 

 

38.8

41.8

32.9

    

 

 

 

42.1

36.4

36.1

    

 

 

 

45.2

39.1

39.2

    

 

 

 

34.8

28.7

29.3

    

 

 

 

48.3

36.4

41.9

    

 

 

 

37.8

36.1

31.7

    

 

 

 

41.1

35.8

35.2

    

 

 

 

43.6

33.7

38.1

    

 

Bonus problem (extra 20pts):

 

 

 

 

 

 

 

 

 

 After reviewing the data from the type of presentation, the team decided to study the effect of two additional factors on the length of call:

 

 

 

a. Gender of the caller

 

 

 

 

 

 

 

 

 

 

b. type of greeting: personal but formal (PF -“Hi, this is Leigh Richardson from the XYZ Times.  May I speak to Mr. Smith?”) Personal but informal (PI-“Hi, this is Leigh Richardson from the XYZ Times.  May I speak to John Smith?”); or impersonal (“I represent the XYZ Times….)

The team acknowledges that in its previous studies, it had controlled for these variables.  Only female callers were selected to participate in the studies, and they were trained to use a personal but informal greeting style.  However, the team wondered if this choice of gender and greeting type was, in fact, best.  The team designed a study in which a total of 30 callers, 15 males and 15 females, were chosen to participate.  The callers were randomly assigned to one of the three greeting-style training groups so that there were five callers in each of the six combinations of the two factors, gender and greeting style.  The callers knew that the team was observing their efforts that evening but didn’t know which particular calls were monitored.  Measurements were taken on the length of call (defined as the difference, in seconds, between the time the person answers the phone and the time he or she hangs up).  Analyze the data and determine the importance of each of the two factors and/or the interaction between them on the length of the call.  Include recommendations for future experiments to perfume.  Do you believe the length of the telephone call is the most appropriate outcome to study?  What other variables should be investigated next?  Be sure to discuss your answer in the discussion section.

 

 

 

 

 

 

 

 

 

 

 

 

 

Greeting

 

 

 

 

 

 

 

 

 

Gender

PF

PI

Impersonal

 

 

 

 

 

 

 

M

45.6

41.7

35.3

 

 

 

 

 

 

 

M

49

42.8

37.7

 

 

 

 

 

 

 

M

41.8

40

41

 

 

 

 

 

 

 

M

35.6

39.6

28.7

 

 

 

 

 

 

 

M

43.4

36

31.8

 

 

 

 

 

 

 

F

44.1

37.9

43.3

 

 

 

 

 

 

 

F

40.8

41.1

40

 

 

 

 

 

 

 

F

46.9

35.8

43.1

 

 

 

 

 

 

 

F

51.8

45.3

39.6

 

 

 

 

 

 

 

F

48.5

40.2

33.2

 

 

 

 

 

 

                                    

 

    • 6 years ago
    Hypothesis Testing With Two Samples Solution
    NOT RATED

    Purchase the answer to view it

    • attachment
      statsolutions2.docx
    • attachment
      statsolutions.xlsx
    • attachment
      bonusproblem.xlsx