Q3 A random sample of 1562 undergraduates enrolled in market

Q3.

A random sample of 1,562 undergraduates enrolled in marketing courses was asked to respond on a scale from one (strongly disagree) to seven (strongly agree) to the proposition: “ Advertising helps raise our standard of living”. The population mean response was 4.27 with a standard deviation of 1.32.

Perform a hypothesis test at a 1% significance level that the population mean response is not equal to 4.

Note: “You can use either the Critical value approach or the p-value approach.” (20 pts)

Solution

3.

Formulating the null and alternative hypotheses,              
              
Ho:   u   =   4  
Ha:    u   =/   4  
              
As we can see, this is a    two   tailed test.      
              
Thus, getting the critical z, as alpha =    0.01   ,      
alpha/2 =    0.005          
zcrit =    +/-   2.575829304      
              
Getting the test statistic, as              
              
X = sample mean =    4.27          
uo = hypothesized mean =    4          
n = sample size =    1562          
s = standard deviation =    1.32          
              
Thus, z = (X - uo) * sqrt(n) / s =    8.084075255          
              
As |z| > 2.576, we   REJECT THE NULL HYPOTHESIS.  

Thus, there is significant evidence that the population mean response is not equal to 4. [CONCLUSION]