Hi Francis,
To get any confidence interval for a population mean, you first need a sample mean. Add up your mercury values in your sample and divide by total sample size. (Sample mean is typically designated xbar)
xbar= (0.58+0.78+0.11+0.99+1.27+0.52+0.94)/7
xbar= 0.74
Now, you also need a sample standard deviation, typically denoted s, but that is complex to calculate manually, so use statistical software, a TI-80s series calculator, or an online calculator:
s=0.38
Now, you do not know population standard deviation, so you must use t. Formula for t confidence interval is:
CI=xbar +/- t*SE
xbar=sample mean
t*=t-critical value obtained from t table or software
SE=standard error, which has it's own formula
SE=s/sqrt(n)
s=sample standard deviation
n=sample size
For this problem:
s=0.38
n=7
SE=0.38/sqrt(7)
SE=0.144
Now, we need another metric, degrees of freedom. For one-sample t test like this:
df=n-1
df=7-1
df=6
Now, go to the t-table, look up 98% in bottom column, 6 in row, and check where they meet. This is your t-critical value, t*
t*= 3.143
Now, we have everything we need to compute our confidence interval:
CI=xbar +/- t*SE
xbar=0.74
t*=3.143
SE=0.144
CI= 0.74 +/- (3.143*0.144)
CI=(0.287, 1.192)
If looking only at the confidence interval, yes, it appears there is too much mercury because it is plausible that true population mean could exceed 1. The upper bound is 1.192. Yet, I would recommend additional sampling in reality because the one fish with 1.27 ppm skews the data. I hope this helps.
