Question

Mercury pollution: Mercury is a toxic metal that is used in many industrial applications. Seven measurements, in milligrams per cubic meter, were taken of the mercury concentration in a lake, with the following results. Assume that the population of measurements is approximately normally distributed.

1.02    1.23    0.91    1.29    1.01    1.35    1.43

Can you conclude that the mean concentration is greater than 1 milligram per cubic meter? Use the α = 0.05 level of significance.

Answer 1

From Given sample ,

$\bar{x}$ = $\sum$ X / n = 1.1771 ,

S = sqrt [ $\sum$ X² - n $\bar{x}$ ² / n-1 ] = 0.1972

H0: $\mu$ <= 1

Ha: $\mu$ > 1

Test statistics

t = ($\bar{x}$ - $\mu$ ) / ( S / sqrt(n) )

= ( 1.1771 -1) / (0.1972 / sqrt(7) )

= 2.38

This is test statistics value.

Critical value at 0.05 level with 6 df = 1.943

Since test statistics falls in rejection region, Reject H0.

We conclude at 0.05 level that we have sufficient evidence to support the claim.