The maximum acceptable level for exposure to microwave radia

The maximum acceptable level for exposure to microwave radiation is 10 mu W/cm2. It is feared that a large television transmitter is polluting a region nearby. A sample of 25 readings is selected at random over a one-week period with a sample mean of X = 10.3 and sample variance of s2 = 4. Calculate the 95% confidence interval for the mean output of the power supplies. Based on your results above would you reject the null hypothesis that the microwave radiation is at an acceptable level? A small computer network consists of ten users and one printer. The average turnaround time for the system is 15 minutes. Ten new users and a second printer are added to the system. A sample of 30 turnaround times for the new network yields an average turnaround time of X = 14 and a sample variance of s2 = 9. Calculate the 95% confidence interval for the mean turnaround time. Is there evidence to support the assertion that the modifications to the system have had no effect on turnaround ti

Solution

I.
a.
Confidence Interval
CI = x ± t a/2 * (sd/ Sqrt(n))
Where,
    x    = Mean
    sd   = Standard Deviation
    a    = 1 - (Confidence Level/100)
    ta/2 = t-table value
    CI   = Confidence Interval
Mean(x)=10.3
Standard deviation( sd )=2
Sample Size(n)=25
Confidence Interval = [ 10.3 ± t a/2 ( 2/ Sqrt ( 25) ) ]
= [ 10.3 - 2.064 * (0.4) , 10.3 + 2.064 * (0.4) ]
= [ 9.47,11.13 ]

b.
YES, We Reject Ho, Lower bound interval is less than 10 W/cm^2