A city health department wishes to find out whether the mean bacteria count per unit volume of water at the lake beach is in the safety level of 200. A researcher gathered 10 water samples of unit volume and found bacteria counts to be 175 190 207 193 184 204 205 193 196 180 The sample mean of observations is 192.7 and sample standard deviation is 10.81. The bacteria counts are normally distributed. We want to test the null hypothesis that mean bacteria count (µ) is 200 aginst the hypothesis that it is less than 200 (where there is no cause for concern).
a) State the null hypothesis and alternative hypothesis
b) Calculate the test statistics
c) Determine the rejection region for the test when? = 0.01?
d) Suppose that the value of the test statistics is 3.21. What decision should be made?