ABC Computers manufacturers network computer server systems and is interested in
ID: 3321471 • Letter: A
Question
ABC Computers manufacturers network computer server systems and is interested in improving its customer support services. As a first step, its marketing department has been charged with the responsibility of summarizing the extent of customer problems in terms of system downtime. The most recent customers were surveyed to determine the amount of downtime (in hours) they had experienced during the previous month. These data are listed below. (Copy and paste into Excel for faster calculations.)
Downtime
43.0
24.9
25.1
25.6
25.8
26.2
25.7
25.6
25.5
26.8
26.9
20.8
26.0
27.4
27.1
27.0
27.5
27.5
27.7
27.7
27.8
27.8
20.4
25.5
27.2
27.2
26.9
27.7
26.9
27.2
27.4
27.1
27.4
ABC wants to include in their new advertising campaign that their computer systems are more reliable than their competitors, XYZ. (XYZ advertise their average system downtime is only 29 hours.) Determine if ABC can advertise that on average their systems are more reliable than XYZ.
(Use 5% significance and assume the standard deviation for all of ABC’s systems is 13 hours.)
Hypotheses: Ho: (Click to select) <=> vs. Ha: (Click to select)=><
(Round t to two decimals and p-value to four)
Test Statistic: t = p-value =
Conclusion: (Click to select)Unable to determineABC's systems are not as reliable as XYZABC's systems are more reliable than XYZXYZ is falsely advertising
If ABC company were to purchase system upgrades that would reduce the standard deviation of downtime by 4 hours, the p-value above would (Click to select)increaseUnable to determinestay the samedecrease. Therefore, you would (Click to select)not recommendrecommend ABC purchase the system upgrades.
Explanation / Answer
Hypotheses: Ho: = 29 hours
Ha : < 29 hours
Here sample size n = 33
sample mean x = 26.8576 hours
population standard deviation = 13 hours
Standard errro of sample mean se = / sqrt(n) = 13/ sqrt(33) = 2.263
Here, population standard deviation is given so we will use Z test here
Test statistic
Z = (x - 29)/ se = (26.8576 - 29)/ 2.263 = -0.9467
p -value = Pr(Z < -0.9467) = 0.1719
so here we will retain the null hpothesis. ABC; system is not more reliable than XYZ systme
Now if standard deviation would be reduced by 4 hours.
New standard deviation = 9
so New, standard error of sample mean = 9/ sqrt(33) = 1.5667
Z = (26.8576 - 29)/ 1.5667 = -1.367
Here Pr(Z < -1.367) = 0.0858 > 0.05
So, still p value is above 0.05 so we would not recommend ABC purchase the sysyem upgrades.