Question

For some reason people care about how acidic fresh water is. Two researchers conducted a study of

15 mountain lakes in the Southern Alps; any lake that has a pH greater than 6 would be classfied as

"non-acidic." Below is a table of the pH levels from the 15 lakes the researchers surveyed:

pH values of 15 Alpine Lakes

7.2 7.3 5.7

7.3 6.3 6.9

6.1 5.5 6.7

6.9 6.3 7.9

6.6 6.5 5.8

The standard deviation of the sample is given as: S = 0:672. At the 5% -level, does this sample

provide sufficient evidence to conclude that, on average, high mountain lakes in the Southern Alps are

non-acidic? State both null and alternative hypotheses, calculate and interpret your test statistic.

Answer 1

Given that,
population mean(u)=6
sample mean, x =6.6
standard deviation, s =0.6719
number (n)=15
null, Ho: μ=6
alternate, H1: μ>6
level of significance, alpha = 0.05
from standard normal table,right tailed t alpha/2 =1.761
since our test is right-tailed
reject Ho, if to > 1.761
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =6.6-6/(0.6719/sqrt(15))
to =3.4585
| to | =3.4585
critical value
the value of |t alpha| with n-1 = 14 d.f is 1.761
we got |to| =3.4585 & | t alpha | =1.761
make decision
hence value of | to | > | t alpha| and here we reject Ho
p-value :right tail - Ha : ( p > 3.4585 ) = 0.00192
hence value of p0.05 > 0.00192,here we reject Ho
------------------------------------------------------------------------------
null, Ho: μ=6
alternate, H1: μ>6
test statistic: 3.4585
critical value: 1.761
decision: reject Ho
p-value: 0.00192
sample provide sufficient evidence to conclude that, on average, high mountain lakes in the southern alps are
non-acidic