Question
In statistical hypothesis testing, null and alternative hypothesis are statements about:
The correct answer is
population parameters
Hypothesis Testing Fundamentals
In statistical hypothesis testing, the primary goal is to draw conclusions about a population using data from a sample. Null and alternative hypotheses are the foundational statements used in this process.
Defining Null and Alternative Hypotheses
- Null Hypothesis (H₀): This is a formal statement asserting that there is no effect, no difference, or no relationship. It represents the status quo or a baseline assumption. Crucially, H₀ always makes a specific claim about a population parameter (e.g., μ = 100, p < 0.5).
- Alternative Hypothesis (H₁ or H<0xE2><0x82><0x90>): This hypothesis contradicts the null hypothesis and represents what the researcher aims to find evidence for. It also makes a claim about the population parameter (e.g., μ ≠ 100, p ≥ 0.5).
Population Parameters vs. Sample Statistics
Understanding the distinction is key:
- Population Parameter: A numerical characteristic of an entire population (e.g., the true average age of all users of a specific app).
- Sample Statistic: A numerical characteristic calculated from a sample drawn from the population (e.g., the average age of 500 users surveyed).
While we use sample statistics (like the sample mean, x̄) to estimate or test hypotheses about population parameters (like the population mean, μ), the hypotheses themselves are always statements concerning the unknown values of the population parameters.
Conclusion
Therefore, both the null hypothesis and the alternative hypothesis are statements about population parameters.
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Important Questions from Hypothesis testing - Teaching
- The null hypothesis in nonparametric test often _______.
1. Includes specification of a population's parameters
2. Is used to evaluate some general population aspect
3. Is very similar to that used in regression analysis
4. Simultaneously tests more than two population parameters - The _______ test determines whether there is a significant difference between the observed and hypothesized distribution for a sample.
1. Independence
2. Coefficient of determination
3. Correlation analysis
4. Goodness-of-fit - Match the LIST-I with LIST-II
LIST-I LIST-II A. One-Tailed Test I. Null hypothesis is rejected if the sample value is significantly higher or lower than the hypothesized value of the population parameter B. Paired difference Test II. A hypothesis test of the difference between the sample means of two independent samples C. Two-Tailed Test III. A sample value significantly above the hypothesized population value will lead to rejection of the null hypothesis D. Upper-Tailed Test IV. Concerned only with whether the observed value deviates from the hypothesized value in one direction
Choose the correct answer from the options given below: - Arrange in correct sequence the steps for testing Statistical Hypothesis :
I. A random sample is drawn from population.
II. Specify the level of significance.
III. Value of the sample statistic is obtained.
IV. Obtained sample statistic is examined with the random sampling distribution of the statistic under consideration.
V. Formulate Null Hypothesis about a parameter of the population, along with an alternate hypothesis.
VI. Retain Null Hypothesis if particular sample outcome is in line with the expected outcomes, otherwise reject it and retain alternate hypothesis.
Codes : - Which set of stoichiometric coefficient correctly balance the equation ?
$$a. H_2O_2 + b. KMnO_4 + c. H_2SO_4 \to d. K_2SO_4 + e. MnSO_4 + f. H_2O + g. O_2$$
Select the correct answer from the codes given below :
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