The maximum acceptable level for exposure to microwave radia

The maximum acceptable level for exposure to microwave radiation is 10 mu W/cm^2. 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 s^2 = 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?

Solution

a)

Note that              
              
Lower Bound = X - t(alpha/2) * s / sqrt(n)              
Upper Bound = X + t(alpha/2) * s / sqrt(n)              
              
where              
alpha/2 = (1 - confidence level)/2 =    0.025          
X = sample mean =    10.3          
t(alpha/2) = critical t for the confidence interval =    2.063898562          
s = sample standard deviation =    2          
n = sample size =    25          
df = n - 1 =    24          
Thus,              
              
Lower bound =    9.474440575          
Upper bound =    11.12555942          
              
Thus, the confidence interval is              
              
(   9.474440575   ,   11.12555942   ) [ANSWER]

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b)

No, we don\'t reject that null hypothesis, as part of the confidence interval is below 10.