Critical Thinking: Communication Skills, EmpiricaVQuantitative Skills A research

Question

Critical Thinking: Communication Skills, EmpiricaVQuantitative Skills 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. nte 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

Explanation / Answer

Given that,
mean(x)=503
standard deviation , s.d1=9.3
number(n1)=50
y(mean)=508.2
standard deviation, s.d2 =9
number(n2)=50
null, Ho: u1 = u2
alternate, H1: u1 < u2
level of significance, = 0.05
from standard normal table,left tailed t /2 =1.677
since our test is left-tailed
reject Ho, if to < -1.677
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =503-508.2/sqrt((86.49/50)+(81/50))
to =-2.8411
| to | =2.8411
critical value
the value of |t | with min (n1-1, n2-1) i.e 49 d.f is 1.677
we got |to| = 2.84115 & | t | = 1.677
make decision
hence value of | to | > | t | and here we reject Ho
p-value:left tail - Ha : ( p < -2.8411 ) = 0.00327
hence value of p0.05 > 0.00327,here we reject Ho
ANSWERS
---------------
1.
null, Ho: u1 = u2
alternate, H1: u1 < u2
test statistic: -2.8411
critical value: -1.677
2.
decision: reject Ho
p-value: 0.00327
3.conclusion:
we have proper evidence to say that reservations made on clour displays were significantly faster.

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