Question

A biologist is worried about a rise in water temperature downstream from a nuclear reactor. If an
increase of more than 3˚ F occurs, the ecosystem may be damaged. Suppose μ is the true average
change in water temperature and that the change in water temperature is normally distributed with
standard deviation of 1˚ F. Eighteen (18) water samples are collected, and the mean temperature
increase for these data is 3.5˚ F.
a) Calculate the test statistic, i.e. z0, to test the hypotheses H0 :μ=3 versus HA :μ>3 .
b) Determine the p-value. (Note that this is a right-tailed test.)
c) State your conclusion, using α =0.05, referring to the specifics of this problem, i.e. what should
the biologist conclude about the water temperature?
d) Do we need the assumption that the change in water temperature is normally distributed? Why
or why not?

Answer 1

a)

z = (xbar - mu)/(sigma/sqrt(n))
= ( 3.5 - 3)/(1/sqrt(18))
= 2.12

b)

p value =0.0169

c)

Reject H0

There is sufficient evidence to support the claim that the water temperature downstream from a nuclear reactor. If an increase of more than 3˚ F occurs,

d)

yes, becaus et The population mean and standard deviation must be known.