MATH 2131 homework
March 21st, 2012
(1) A test of the null hypothesis H
0 if the alternative is
(a)
(b)
(c)
H a
H a
H a
: µ > µ
0
: µ < µ
0
: µ = µ
0
: µ = µ
0 gives test statistics z obs
= 1 .
34 .
Find the p-value
(2) Statistics can help decide the authorship of literary works. Sonnets by a certain Elizabethan poet are known to contain an average of µ = 8 .
9 new words (words not used in the poet’s other works). The standard deviation of the number of new words is σ = 2 .
5 .
A manuscript with 6 new sonnets has come to light, and scholars are debating whether it is the poet’s work. The new sonnets contain an average of ¯ = 10 .
2 words not used in the poet’s known works. We expect poems by another author to contain more new words, so to see if we have evidence that the new sonnets are not by our poet we do a hypothesis test.
(a) Give the z test statistic and calculate the p-value. What do you conclude?
(b) What is the power of the test under the alternative µ = 12?
(c) How large a sample size is necessary so that the power of the test under the alternative µ = 12 is at least 95%?
(3) The level of calcium in the blood in healthy young adults varies with mean about 9.5 milligrams per deciliter and standard deviation of about σ = 0 .
4 .
A clinic in rural Guatemala measures the blood calcium level of 160 health pregnant women at their first visit for prenatal care. The mean is ¯ = 9 .
57 .
Is this an indication that the mean calcium level in the population from which these women came differs from 9.5? What is the power of this test at one standard deviation away from the mean? What is it at two standard deviations?
(4) You are told that a significance test is significant at the 5% level. From this information can you determine whether or not it is significant at the 1% level? Explain your answer.
(5) According to data from the Tobacco Institute Testing Lab, Camel Lights King Size cigarettes contain an average of 1.4 milligrams of nicotine. An advocacy group commissions an independent test to see if the mean nicotine content is higher than the industry laboratory claims.
(a) What are H
0 and H a
?
(b) Suppose that the test statistics is z = 2 .
36 .
Is this result significant at the 5% level?
(c) Is the result significant at the 1% level?
(d) What is the p-value?
(e) What is the power of this test? Explain your answer.