Textbook Question
Identifying a Test In Exercises 21–24, determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed.
Ha: p = 0.25
H0: p ≠ 0.25
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9. Hypothesis Testing for One Sample
Steps in Hypothesis Testing
2:17 minutesProblem 11.1.4
Textbook Question
In your own words, explain why the hypothesis test discussed in this section is called the sign test.
Verified step by step guidance1
The sign test is a non-parametric statistical test used to evaluate the median of a population or to compare paired data without making assumptions about the data's distribution.
It is called the 'sign test' because it focuses on the signs (+ or -) of the differences between paired observations or the deviations of data points from a hypothesized median.
For each data point, the test determines whether the value is above (+) or below (-) the hypothesized median, ignoring the actual magnitude of the differences.
The test then counts the number of positive and negative signs to assess whether there is a significant deviation from the hypothesized median or equality in paired data.
This approach makes the sign test robust and applicable to data that do not meet the assumptions of normality or other parametric tests.
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Video duration:
2mKey Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Hypothesis Testing
Hypothesis testing is a statistical method used to make decisions about a population based on sample data. It involves formulating a null hypothesis (H0) and an alternative hypothesis (H1), then using sample data to determine whether there is enough evidence to reject H0 in favor of H1. This process helps researchers draw conclusions about the population while controlling for error rates.
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Step 1: Write Hypotheses
Sign Test
The sign test is a non-parametric statistical test used to evaluate the median of a population. It is particularly useful when the data does not meet the assumptions required for parametric tests, such as normality. The test works by comparing the signs (positive or negative) of differences between paired observations, making it a straightforward method for hypothesis testing without relying on specific distributional assumptions.
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Non-parametric Tests
Non-parametric tests are statistical tests that do not assume a specific distribution for the data. They are often used when the sample size is small or when the data is ordinal or not normally distributed. The sign test is an example of a non-parametric test, as it focuses on the ranks or signs of the data rather than the actual values, allowing for more flexibility in analysis.
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