Question

In a survey on corporate​ ethics, a poll split a sample at​ random, asking 500 faculty and corporate recruiters the​ question: "Generally​ speaking, do you believe that MBAs are more or less aware of ethical issues in business today than five years​ ago?" The other half were​ asked: "Generally​ speaking, do you believe that MBAs are less or more aware of ethical issues in business today than five years​ ago?"

1) These may seem like the same​ question, but sometimes the order of the choices in a question matters. In response to the first​ question, more than 50% thought MBA graduates were more aware of ethical​ issues, but when the question was phrased​ differently, this proportion was less than 50% . The difference in these statistics is (pick one and explain briefly).

A. probably due to some random error

B. probably due to response bias

​

2) Each group consisted of 400 respondents. We can combine​ them (considering the overall group to be one larger random​ sample) to find a 90% confidence interval for the parameter of interest (here, the proportion of the faculty and corporate recruiters that believe MBAs are more aware of ethical issues​ today). .Overall (i.e. in the larger random sample), 48% believed MBAs are more aware of ethical issues​ today .

2a) Construct a 90% confidence interval. Show all your work.

2b) The margin of error in the above calculation is equal to ____________________________.

Answer 1

1) B. probably due to response bias

2)

a)

Level of Significance,   α =    0.10          
Sample Size,   n =    400          
                  
Sample Proportion ,    p̂ = x/n =    0.4800          
z -value =   Zα/2 =    1.645   [excel formula =NORMSINV(α/2)]      
                  
Standard Error ,    SE = √[p̂(1-p̂)/n] =    0.0250          
margin of error , E = Z*SE =    1.645   *   0.0250   =   0.0411
                  
90%   Confidence Interval is              
Interval Lower Limit = p̂ - E =    0.480   -   0.0411   =   0.439
Interval Upper Limit = p̂ + E =   0.480   +   0.0411   =   0.521
                  
90%   confidence interval is (   0.4389   < p <    0.5211   )

b)

margin of error , E = Z*SE =    1.645   *   0.0250   =   0.0411