The Average Magnesium Concentration in Ground Water Around Metro City $\mu = 59.3$

The average magnesium concentration in ground water around Metro City is $\mu = 59.3$ parts per million (ppm) with a standard deviation of $\sigma = 18$ . The table below shows the ground-water magnesium concentrations $( \mathrm { ppm } )$ from random sites in a suburb located 15 miles away. At $\alpha = 0.10$ , can it be concluded that the average magnesium concentration in the suburb differs from $59.3 \mathrm { ppm }$ ? 43 62 56 32 36
116 27 9 47 111
115 96 27 55 79
59 63 43 36 44
102 54 32 64 93
78 8 105 110 84
124 125 104 104 87
a. State the hypotheses and identify the claim.
b. Find the critical values.
c. Compute the test statistic.
d. Make a decision.
e. Summarize the results.