Question

Water samples are taken from water used for cooling as it is being discharged from a power plant into a river. It has been determined that as long as the mean temperature of the discharged water is at most 150 degrees Fahrenheit, there will be no negative effects on the river ecosystem. To investigate whether the power plant is in compliance with regulations that prohibit a mean discharge water temperature above 150 degrees, a scientist will take 50 water samples at randomly selected times and will record the water temperature of each sample. She will then use a Z statistic ?=, "-./0 1√3 4 to decide between the hypothesis H0: ?=150 and H1: ?>150 where ? is the true mean temperature of the discharged water. Assume that ? is known to be 10 degrees.

(a) Explain why a Z statistic is appropriate in this setting?

(b) Suppose that the Critical Value Decision Rule is: Reject H0 if
Z ≥ 1.75. What significance level does this rule correspond to?
Round to the nearest percentage point.

(c) Suppose that the Critical Value Decision Rule is: Reject H0 if
Z ≥ 1.75. What is the rejection region for this test in terms of ?
"? (In other words: for what values of ? " will you reject H0?)

(d) Suppose that the sample mean from the 50 water samples is ? "=152.1 degrees. If H0 is rejected if Z ≥ 1.75 then what is the appropriate conclusion for this test? Write your conclusion and justify it.

(e) Suppose that the true value of ? is 153 degrees (i.e., this
means that the alternative hypothesis is actually true) and that
you reject H0 if Z ≥ 1.75. What is the power of this test?

Answer #1

(a) Since sample size is large and is known

z statistic is appropriate

(b) from z table , the area from 1.75 and beyond is 0.0401

significance level is 4.01%

(c) we know that

when z = 1.75 , , n = 50

X'' = 152.47

(d)

= 1.48

since calculated value of z (test statistic) is less than 1.75

we fail to reject H0

There is not enough evidence to conclude that mean temp of discharged water more than 150 degrees

(e) Power = P(rejecting H0 I H1 true)

=

=

= P(Z > -0.37) = 0.6443

power = 0.6443

Consolidated Power, a large electric power utility, has just
built a modern nuclear power plant. This plant discharges waste
water that is allowed to flow into the Atlantic Ocean. The
Environmental Protection Agency (EPA) has ordered that the waste
water may not be excessively warm so that thermal pollution of the
marine environment near the plant can be avoided. Because of this
order, the waste water is allowed to cool in specially constructed
ponds and is then released into the...

Consolidated Power, a large electric power utility, has just
built a modern nuclear power plant. This plant discharges waste
water that is allowed to flow into the Atlantic Ocean. The
Environmental Protection Agency (EPA) has ordered that the waste
water may not be excessively warm so that thermal pollution of the
marine environment near the plant can be avoided. Because of this
order, the waste water is allowed to cool in specially constructed
ponds and is then released into the...

Consolidated Power, a large electric power utility, has just
built a modern nuclear power plant. This plant discharges waste
water that is allowed to flow into the Atlantic Ocean. The
Environmental Protection Agency (EPA) has ordered that the waste
water may not be excessively warm so that thermal pollution of the
marine environment near the plant can be avoided. Because of this
order, the waste water is allowed to cool in specially constructed
ponds and is then released into the...

The carapace lengths (in mm) of crayfish were recorded for
samples from two sections of a stream
in Kansas.
section1 5, 11, 16, 8, 12
section2 17, 14,15, 21,19, 13
Use the data in problem above to test for a difference between
the two sections using the Mann-Whitney U test.
a. Cite the critical values (from Table A4) for a two-sided test
at α = 0.05. Remember that the critical-values given in the table
are for one-sided tests. Write a...

] X~NORM(44.0, 3.2). A sample mean of 46.7 is taken, for n=30.
Given H0: m=44.0, H1: m > 44.0, and
a=0.05. Note this is a test on the mean for a single population.
What test statistic should be used? (Z, T, c2, F?)?
Why?
What is the critical value of the test statistic to
use for this test? What is the accept region (accept H0)
and reject region (reject H0)?
Based on the critical value, what is your conclusion regarding...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 10 minutes ago

asked 24 minutes ago

asked 39 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago