Your company is evaluating two cloud-based secured data storage services. “Pie i
ID: 3309831 • Letter: Y
Question
Your company is evaluating two cloud-based secured data storage services. “Pie in the Sky,” the newer service, claims its uploading and downloading speeds are faster than the older service, “Cloudy but Steady Skies.” You need to make a decision based on published access times for both services at different times and for varying file sizes. To make your decision, you purchase a statistical study, which indicates that average download time for Pie in the Sky is 0.77 sec. per MB and for Cloudy but Steady Skies is 0.84. Assume that n1 = n2 = 50,1 = 0.2 and 2 = 0.3. With = .05, the appropriate decision is ______.
reject the null hypothesis 12 < 22
accept the alternate hypothesis 1 2 > 0
reject the alternate hypothesis n1 = n2 = 50
fail to reject the null hypothesis 1 2 = 0
do nothing
reject the null hypothesis 12 < 22
accept the alternate hypothesis 1 2 > 0
reject the alternate hypothesis n1 = n2 = 50
fail to reject the null hypothesis 1 2 = 0
do nothing
Explanation / Answer
Given that,
mean(x)=0.77
standard deviation , 1 =0.2
number(n1)=50
y(mean)=0.84
standard deviation, 2 =0.3
number(n2)=50
null, Ho: u1 = u2
alternate, H1: 1 != u2
level of significance, = 0.05
from standard normal table, two tailed z /2 =1.96
since our test is two-tailed
reject Ho, if zo < -1.96 OR if zo > 1.96
we use test statistic (z) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
zo=0.77-0.84/sqrt((0.04/50)+(0.09/50))
zo =-1.373
| zo | =1.373
critical value
the value of |z | at los 0.05% is 1.96
we got |zo | =1.373 & | z | =1.96
make decision
hence value of | zo | < | z | and here we do not reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != -1.373 ) = 0.16981
hence value of p0.05 < 0.16981,here we do not reject Ho
ANSWERS
---------------
null, Ho: u1 = u2
alternate, H1: 1 != u2
test statistic: -1.373
critical value: -1.96 , 1.96
decision: do not reject Ho
p-value: 0.16981
fail to reject the null hypothesis 1 2 = 0
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