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Chapter 7: Q20E (page 403)
If a hypothesis test were conducted using 伪= 0.05, for which of the following p-values would the null hypothesis be rejected?
a. .06
b. .10
c. .01
d. .001
e. .251
f. .042
The null hypothesis would be rejected for every case because all of the given p-values are less than the 伪 value.
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For each of the following rejection regions, sketch the sampling distribution for z and indicate the location of the rejection region.
a. \({H_0}:\mu \le {\mu _0}\) and \({H_a}:\mu > {\mu _0};\alpha = 0.1\)
b. \({H_0}:\mu \le {\mu _0}\) and \({H_a}:\mu > {\mu _0};\alpha = 0.05\)
c. \({H_0}:\mu \ge {\mu _0}\) and \({H_a}:\mu < {\mu _0};\alpha = 0.01\)
d. \({H_0}:\mu = {\mu _0}\) and \({H_a}:\mu \ne {\mu _0};\alpha = 0.05\)
e. \({H_0}:\mu = {\mu _0}\) and \({H_a}:\mu \ne {\mu _0};\alpha = 0.1\)
f. \({H_0}:\mu = {\mu _0}\) and \({H_a}:\mu \ne {\mu _0};\alpha = 0.01\)
g. For each rejection region specified in parts a鈥揻, state the probability notation in z and its respective Type I error value.
A random sample of n observations is selected from a normal population to test the null hypothesis that 碌=10.Specify the rejection region for each of the following combinations of \(Ha,\alpha ,\) and n:
a.\(Ha:\)碌\( \ne 10;\alpha = .05.;n = 14\)
b.\(Ha:\)碌\( > 10;\alpha = .01;n = 24\)\(\)
c.\(Ha:\)碌\( > 10;\alpha = .10;n = 9\)
d.\(Ha:\)碌 <\(10:\alpha = .01;n = 12\)
e.\(Ha:\)碌\( \ne 10;\alpha = .10;n = 20\)
f. \(Ha:\)碌<\(10;\alpha = .05;n = 4\)
Refer to Exercise 6.44 (p. 356), in which 50 consumers taste-tested a new snack food. Their responses (where 0 = do not like; 1 = like; 2 = indifferent) are reproduced below
An analyst tested the null hypothesis that 渭 鈮� 20against the alternative hypothesis that 渭 <20. The analyst reported a p-value of .06. What is the smallest value of伪for which the null hypothesis would be rejected?
Specify the differences between a large-sample and a small-sample test of a hypothesis about a population mean m. Focus on the assumptions and test statistics.
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