The parameter value in the null hypothesis is called a _ and the value does not come from a _.
The correct answer and explanation is:
Correct Answer:
Test value; sample
Explanation (300 words):
In hypothesis testing, the null hypothesis (H₀) is a statement that there is no effect or no difference, and it includes a specific value for a population parameter (like a mean or proportion). The number provided in the null hypothesis is called the test value.
This test value is a fixed number used as a reference point for comparing sample data. It is important to understand that this value does not come from the sample. Instead, it is a value we assume to be true under the null hypothesis — often based on past research, theory, or a standard benchmark.
On the other hand, sample values are computed from observed data. These include the sample mean, sample proportion, or other sample statistics, and they are used to test how consistent the observed data is with the assumed parameter in the null hypothesis.
For example, suppose a company claims its batteries last 10 hours on average. This claim becomes the null hypothesis:
H₀: μ = 10
Here, 10 is the test value, and it is not derived from the sample. The researcher then collects sample data (say, the average battery life of 30 batteries) and calculates a sample mean. The sample mean is then compared to the test value to determine if there’s enough evidence to reject the null hypothesis.
To summarize:
- The parameter value in the null hypothesis is called the test value.
- This value does not come from the sample; it is a claim or assumption about the population.
- The sample statistic is then used to assess the validity of this claim through a hypothesis test.