Question

Example 2. A stream has been monitored unit for a number of years, and the total dissolved solids in the stream average 40 parts per million. Following a recent change in land use in the drainage basin of the stream, a fluvial geomorphologist finds that the mean parts per million of dissolved solids in a 25-week sample is 52, with a sample standard deviation of 32. Has there been a change in the average level of dissolved solids in this stream? Assume a normal population and that α = .10.

Answer 1

H0: $\mu$ = 40

Ha: $\mu$ $\neq$ 40

Test statistics

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

= ( 52 - 40) / ( 32 / sqrt ( 25 ) )

= 1.88

Critical value at 0.10 level with 24 df = -1.711 , 1.711

Since test statistics > 1.711, Reject H0.

We conclude at 0.10 level that we have sufficient evidence to support the claim that  there has been a change

in the average level of dissolved solids in this stream.