Math Problem Statement
A certain drug is used to treat asthma. In a clinical trial of the drug,
2020
of
267267
treated subjects experienced headaches (based on data from the manufacturer). The accompanying calculator display shows results from a test of the claim that less than
1111%
of treated subjects experienced headaches. Use the normal distribution as an approximation to the binomial distribution and assume a
0.050.05
significance level to complete parts (a) through (e) below.
1-PropZTest
propless than<0.110.11
zequals=negative 1.832705209−1.832705209
pequals=0.03342321110.0334232111
ModifyingAbove p with caretpequals=0.07490636700.0749063670
nequals=267267
Question content area bottom
Part 1
a. Is the test two-tailed, left-tailed, or right-tailed?
Right tailed test
Two-tailed test
Left-tailed test
Solution
To determine whether the test is two-tailed, left-tailed, or right-tailed, we need to understand the nature of the claim being tested.
In this case, the claim is that "less than 11% of treated subjects experienced headaches."
This implies that the test is:
- Left-tailed test: because we are testing if the proportion is less than 0.11 (11%).
Given the context of the problem and the claim, we can conclude that the test is left-tailed.
If you have any more questions or need further details, feel free to ask!
Here are some related questions you might be interested in:
- How do you interpret the z-value in a hypothesis test?
- What does the p-value indicate in this context?
- How do you calculate the test statistic for a proportion test?
- What assumptions must be met to use the normal distribution as an approximation to the binomial distribution?
- How do you determine the significance level in hypothesis testing?
Tip: In hypothesis testing, clearly understanding the direction of the test (left-tailed, right-tailed, or two-tailed) is crucial, as it influences how you interpret the test statistic and p-value.
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Math Problem Analysis
Mathematical Concepts
Hypothesis Testing
Normal Distribution Approximation
Proportion Tests
Formulas
1-PropZTest formula: Z = (p̂ - p0) / sqrt(p0(1-p0)/n)
Theorems
Normal Approximation to the Binomial Distribution
Hypothesis Testing for Proportions
Suitable Grade Level
Grades 11-12
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