a. Weatherwise is a magazine published by the American Meteorological Society. One issue gives a rating system used to classify Nor'easter storms that frequently hit New England and can cause much damage near the ocean. A severe storm has an average peak wave height of μ = 16.4 feet for waves hitting the shore. Suppose that a Nor'easter is in progress at the severe storm class rating. Peak wave heights are usually measured from land (using binoculars) off fixed cement piers. Suppose that a reading of 34 waves showed an average wave height of x = 17.3 feet. Previous studies of severe storms indicate that σ = 3.5 feet. Does this information suggest that the storm is (perhaps temporarily) increasing above the severe rating? Use α = 0.01. Solve the problem using the critical region method of testing (i.e., traditional method). (Round your answers to two decimal places.)
test statistic = critical value =
b.The Student's t distribution table gives critical
values for the Student's t distribution. Use an
appropriate d.f. as the row header. For a
right-tailed test, the column header is the value of
α found in the one-tail area row. For a
left-tailed test, the column header is the value of
α found in the one-tail area row, but you must
change the sign of the critical value t to −t.
For a two-tailed test, the column header is the value of
α from the two-tail area row. The critical values
are the ±t values shown.
A random sample of 51 adult coyotes in a region of northern
Minnesota showed the average age to be x = 2.15 years,
with sample standard deviation s = 0.75 years. However, it
is thought that the overall population mean age of coyotes is
μ = 1.75. Do the sample data indicate that coyotes in this
region of northern Minnesota tend to live longer than the average
of 1.75 years? Use α = 0.01. Solve the problem using the
critical region method of testing (i.e., traditional method).
(Round your answers to three decimal places.)
| test statistic | = | |
| critical value |
c.The Student's t distribution table gives critical
values for the Student's t distribution. Use an
appropriate d.f. as the row header. For a
right-tailed test, the column header is the value of
α found in the one-tail area row. For a
left-tailed test, the column header is the value of
α found in the one-tail area row, but you must
change the sign of the critical value t to −t.
For a two-tailed test, the column header is the value of
α from the two-tail area row. The critical values
are the ±t values shown.
Let x be a random variable that represents the pH of
arterial plasma (i.e., acidity of the blood). For healthy adults,
the mean of the x distribution is μ = 7.4†. A new
drug for arthritis has been developed. However, it is thought that
this drug may change blood pH. A random sample of 41 patients with
arthritis took the drug for 3 months. Blood tests showed that
x = 8.0 with sample standard deviation s = 1.7.
Use a 5% level of significance to test the claim that the drug has
changed (either way) the mean pH level of the blood. Solve the
problem using the critical region method of testing (i.e.,
traditional method). (Round your answers to three decimal
places.)
| test statistic | = | |
| critical value | = ± |
a.
Null and alternate hypotheses.
H0: = 16.4
H1 > 16.4
sample test statistic:
z-statistic = (17.3 - 16.4) / (3.5 / sqrt 34) = 1.499
Using Excel function =NORMSINV(0.99) we will get critical z value 2.33 for right tailed test.
Conclusion :
There is insufficient evidence at the 0.01 level to reject the claim that the storm is not increasing above the severe rating.
Please post remaining questions separately.
Hope this will be helpful. Thanks and God Bless You :)
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