A researcher was tasked with determining whether the video display used by trave
ID: 3229862 • Letter: A
Question
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.
On your own paper write a report to the travel agency explaining your results. Use complete sentences and proper grammar. your report should be a minimum of 2 sentences.
Explanation / Answer
Solution:-
Given, Fifty subjects were tested (n1 = 50) with color displays (x-bar1 = 503 sec, s1 = 9.3 sec) and fifty subjects were tested (n2 = 50) with black and white displays (x-bar2 = 508.2 sec, s2 = 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.
The solution to this problem takes four steps: (1) state the hypotheses, (2) formulate an analysis plan, (3) analyze sample data, and (4) interpret results. We work through those steps below:
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: 1 - 2 = 0
Alternative hypothesis: 1 - 2 0
Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the difference between sample means is too big or if it is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a two-sample t-test of the null hypothesis.
Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).
SE = sqrt[(s12/n1) + (s22/n2)]
SE = sqrt[(9.32/50) + (9.02/50] = 1.83
DF = (s12/n1 + s22/n2)2 / { [ (s12 / n1)2 / (n1 - 1) ] + [ (s22 / n2)2 / (n2 - 1) ] }
DF = (9.32/50 + 9.02/50)2 / { [ (9.32 / 50)2 / (49) ] + [ (9.02 / 50)2 / (49) ] }
DF = 11.22 / (0.061 + 0.054) = 97.565
t = [ (x1 - x2) - d ] / SE = [ (503 - 508.2) - 0 ] / 1.83 = -2.84
where s1 is the standard deviation of sample 1, s2 is the standard deviation of sample 2, n1 is the size of sample 1, n2 is the size of sample 2, x1 is the mean of sample 1, x2 is the mean of sample 2, d is the hypothesized difference between the population means, and SE is the standard error.
Since we have a two-tailed test, the P-value is the probability that a t statistic having 98 degrees of freedom is more extreme than -2.84; that is, less than -2.84 or greater than 2.84.
We use the t Distribution Calculator to find P(t < -2.84)
The P-Value is 0.005487.
The result is significant at p < 0.05
Interpret results. Since the P-value (0.005487) is less than the significance level (0.05), we cannot accept the null hypothesis. Thus accepting the alternate hypothesis, we can conclude that 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.
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