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 :
Statistical Hypothesis Testing: Correct Sequence
The process of testing a statistical hypothesis involves a series of logical steps. Arranging these steps correctly is crucial for a valid analysis. The standard sequence ensures that assumptions are stated before data is analyzed and decisions are based on predefined criteria.
Logical Order of Hypothesis Testing Steps
- V. Formulate Hypotheses: The process begins by clearly defining the null hypothesis ($H_0$), which represents a statement of no effect or no difference, and the alternate hypothesis ($H_a$), which is what we suspect might be true.
- II. Specify the Level of Significance ($\alpha$): Before examining the data, determine the acceptable probability of rejecting the null hypothesis when it is actually true (Type I error). Common levels are 0.05 or 0.01.
- I. Draw Random Sample: Collect a representative sample from the population of interest. Random sampling helps ensure the sample reflects the population characteristics.
- III. Obtain Sample Statistic: Calculate the value of the relevant statistic (e.g., sample mean, sample proportion) from the data collected in the random sample.
- IV. Examine Sample Statistic: Compare the obtained sample statistic's value against the sampling distribution of that statistic, assuming the null hypothesis ($H_0$) is true. This step often involves calculating a test statistic and determining its corresponding p-value.
- VI. Make Decision: Based on the comparison in the previous step (e.g., comparing the p-value to the significance level $\alpha$), decide whether to reject the null hypothesis ($H_0$) in favor of the alternate hypothesis ($H_a$) or to retain the null hypothesis if the sample outcome is consistent with it.
Therefore, the correct sequence is V, II, I, III, IV, VI.
Important Questions from Hypothesis testing - Teaching
- Type II error occurs when :
- 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: - The null hypothesis that all slope coefficients are simultaneously equal to zero is tested in logit model by:
