MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
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In a large clinical trial, 399,935 children were randomly assigned to two groups. The treatment group consisted of
198,188 children given a vaccine for a certain disease, and 27 of those children developed the disease. The other
201,747 children were given a placebo, and 83 of those children developed the disease. Consider the vaccine
treatment group to be the first sample. Complete parts (a) through (d) below.
a. Assume that a 0.01 significance level will be used to test the claim that p, <p2. Which is better: A hypothesis test
or a confidence interval?
is better.
Transcribed Image Text:In a large clinical trial, 399,935 children were randomly assigned to two groups. The treatment group consisted of 198,188 children given a vaccine for a certain disease, and 27 of those children developed the disease. The other 201,747 children were given a placebo, and 83 of those children developed the disease. Consider the vaccine treatment group to be the first sample. Complete parts (a) through (d) below. a. Assume that a 0.01 significance level will be used to test the claim that p, <p2. Which is better: A hypothesis test or a confidence interval? is better.
b. In general, when dealing with inferences for two population proportions, which two of the following are equivalent:
confidence interval method; P-value method; critical value method?
P-value method and critical value method
are equivalent, in that they will always lead to the same
conclusion. Both of these methods use a standard deviation based on
the assumption that the two population proportions are equal, whereas the other method uses a standard
deviation based on estimated values of the population proportions.
c. If a 0.05 significance level is to be used to test the claim that p, <p2, what confidence level should be used?
90 %
(Type an integer or a decimal.)
d. If the claim in part (c) is tested using this sample data, we get this confidence interval:
- 0.000613 < p, - p2 < - 0.000391. What does this confidence interval suggest about the claim?
Because the confidence interval does not contain
0,
there
appears to be
a
significant difference between the two proportions. Because the confidence interval consists
only of values less than
0,
it appears that the first proportion is
less than
the second proportion. There is
sufficient evidence to support the claim that the
rate of polio is less for children given the vaccine than it is for children given a placebo.
Transcribed Image Text:b. In general, when dealing with inferences for two population proportions, which two of the following are equivalent: confidence interval method; P-value method; critical value method? P-value method and critical value method are equivalent, in that they will always lead to the same conclusion. Both of these methods use a standard deviation based on the assumption that the two population proportions are equal, whereas the other method uses a standard deviation based on estimated values of the population proportions. c. If a 0.05 significance level is to be used to test the claim that p, <p2, what confidence level should be used? 90 % (Type an integer or a decimal.) d. If the claim in part (c) is tested using this sample data, we get this confidence interval: - 0.000613 < p, - p2 < - 0.000391. What does this confidence interval suggest about the claim? Because the confidence interval does not contain 0, there appears to be a significant difference between the two proportions. Because the confidence interval consists only of values less than 0, it appears that the first proportion is less than the second proportion. There is sufficient evidence to support the claim that the rate of polio is less for children given the vaccine than it is for children given a placebo.
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