Question
student's t-test is useful for testing the A. significance of difference between two sample means B. independence of attributes C. significance of correlation coefficient D. analysis of variance Choose the correct answer from the options given below:
The correct answer is
A and C Only
Student's t-test Applications
The student's t-test is a fundamental statistical hypothesis test used primarily to analyze differences between two groups. Its key applications are:
- Significance of Difference Between Two Sample Means: This is the core function of the t-test. It helps determine if the difference observed between the means of two separate samples (or paired observations) is likely due to chance or represents a genuine difference in the populations from which the samples were drawn.
- Significance of Correlation Coefficient: A t-test can also evaluate whether a calculated correlation coefficient (e.g., Pearson's r) between two variables is statistically significant. This tests the hypothesis that the true population correlation is zero, meaning there is no linear association.
Other statistical methods are used for different purposes:
- Independence of Attributes: Typically assessed using the Chi-square ($\chi^2$) test, not the t-test.
- Analysis of Variance (ANOVA): Used for comparing means across three or more groups. While related, it's distinct from the t-test's focus on two groups.
Based on these applications, the student's t-test is useful for testing the significance of the difference between two sample means and the significance of a correlation coefficient.
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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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