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A city health department wishes to determine if the mean bacteria count per unit volume of water at a lake beach is below the safety level of 200. Bacteria levels in the lake are typically normally distributed. A researcher collected 10 water samples of unit volume and found mean and standard deviation of bacteria counts as 192.7 and 10.8, respectively.
(i) Is this a one-sided or two-sided test, why?
(ii) Do the data indicate that there is no cause of concern (assume a=0.05)?
(iii) Do the data indicate that there is no cause of concern if a=0.01?
(iv) What is the p-value for the test statistic calculated in (ii), and what do you conclude about the null hypothesis for a=0.01 & α=0.05?
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