A researcher was tasked with determining whether the video display used by trave

Question

A researcher was tasked with determining whether the video display used by travel agents toe booking airline reservations should be in color or in black and white. Market research has shown that travel agencies were primarily concerned with the speed at which reservations can be made. Therefore, the question was whether color displays allow travel agents to book reservations faster Fifty subjects were tested with color displays (x-bar = 503 sec. s = 9 3 sec) and fifty subjects were tested with black and white displays (x-bar = 508.2 sec. s = 9 0 sec). Test if the reservations made on the color displays were significantly faster (less time) than those made on the black and white displays at a significance level of 0 05. Write the null and alternative hypothesis. Would you reject the null hypothesis? Justify your answer using a complete sentence and proper grammar. Be sure to show the statistics that were used to make your decision.

Explanation / Answer

1.

Formulating the null and alternative hypotheses,              
              
Ho:   u1 - u2   >=   0  
Ha:   u1 - u2   <   0   [ANSWER]

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2.

At level of significance =    0.05          

As we can see, this is a    left   tailed test.      
Calculating the means of each group,              
              
X1 =    503          
X2 =    508.2          
              
Calculating the standard deviations of each group,              
              
s1 =    9.3          
s2 =    9          
              
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):              
              
n1 = sample size of group 1 =    50          
n2 = sample size of group 2 =    50          
Thus, df = n1 + n2 - 2 =    98          
Also, sD =    1.830245885          
              
Thus, the t statistic will be              
              
t = [X1 - X2 - uD]/sD =    -2.841148308          
              
where uD = hypothesized difference =    0          
              
Now, the critical value for t is              
              
tcrit =    -   1.660551217      
              
              
Also, using p values,              
              
p =    0.002734157          
              
As |t| > 1.6605, and P < 0.05,    WE REJECT THE NULL HYPOTHESIS.          

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3.

There is significant evidence that the reservations made on the color displays were significantly faster than thse made o the balck and white displays at 0.05 level. [CONCLUSION]

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