A researcher was tasked with determining whether the video d

A researcher was tasked with determining whether the video display used by travel agents for

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.

1. Write the null and alternative hypothesis.

2. 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.

3. Write out the final conclusion for this hypothesis test as you would present it to the travel agency.

Use complete sentences and proper grammar.

Lab Ch.11 continued

The agencies, however, are not concerned with statistical significance. The agencies would like to

know if the difference in speed is of practical importance to them. Market research has shown that in

order to justify the higher price of color displays, they must be faster by an average of at least 10

seconds per transaction.

4. Construct a 90% confidence interval for the difference in the means (color minus black and white).

the customer complaints?

5. Use the interval to explain to the agencies if they should or should not pay for color displays.

Use complete sentences and proper grammar.

Solution

1.

Let

u1 = mean of color displays
u2 = mean of clack and white

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          

Also, sD =    1.830245885          
              
Thus, the z statistic will be              
              
z = [X1 - X2 - uD]/sD =    -2.841148308          
              
where uD = hypothesized difference =    0          
              
Now, the critical value for z is              
              
zcrit =    -   1.645
              
As z < 1.645, we Reject the null hypothesis. [ANSWER]

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3.

Thus, there is significant evidence that 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.

              
              
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4.

              
For the   0.9   confidence level, then      
              
alpha/2 = (1 - confidence level)/2 =    0.05          
z(alpha/2) =    1.644853627          
              
lower bound = [X1 - X2] - z(alpha/2) * sD =    -8.210486582          
upper bound = [X1 - X2] + z(alpha/2) * sD =    -2.189513418          
              
Thus, the confidence interval is              
              
(   -8.210486582   ,   -2.189513418   ) [ANSWER]

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5.

As this interval is totally less than 0, then there is significant evidence that the differences in time is negative, hence a faster time.

Thus, they should pay for color displays.