Testing of Hypothesis MCQ Quiz in தமிழ் - Objective Question with Answer for Testing of Hypothesis - இலவச PDF ஐப் பதிவிறக்கவும்

Key Points

• In hypothesis testing, the null hypothesis (H0) is the assumption that there is no significant difference between the means of the two groups being compared.
• On the other hand, the research hypothesis (Ha or H1) is the assumption that there is a significant difference between the means of the two groups being compared.
• In this case, the researcher has calculated a t-value and found it to be significant at the 0.05 level. This means that the difference between the means of the two groups is unlikely to have occurred by chance, and there is evidence to suggest that the means of the two groups are significantly different from each other.
• If the t-value had not been significant, then the null hypothesis would have been retained, indicating that there is no significant difference between the means of the two groups.
• However, since the t-value is significant, the null hypothesis can be rejected, and the research hypothesis can be retained. This means that there is evidence to suggest that there is a significant difference between the means of the two groups being compared.

Therefore, the correct statement is 2) Null hypothesis may be rejected and Research hypothesis may be retained.

Key PointsChi-square test:

• The chi-square goodness-of-fit test is used to determine whether an observed frequency distribution matches an expected frequency distribution.
• In this case, the researcher would use the test to compare the observed distribution of student attendance throughout the academic year with an expected distribution that assumes attendance is randomly distributed.
• The expected distribution could be calculated based on the total number of classes or days in the academic year, and assuming an equal probability of attendance for each day.
• The observed distribution could be calculated by recording the actual attendance of a sample of students throughout the year.
• If the chi-square test indicates that the observed distribution significantly differs from the expected distribution, this would suggest that attendance is not randomly distributed throughout the academic year.
• On the other hand, if the test indicates that the observed distribution does not significantly differ from the expected distribution, this would suggest that attendance is randomly distributed throughout the year.

Therefore, the appropriate statistical test for this research question would be the chi-square goodness-of-fit test.

Key Points

• Parametric tests assume that the data being analyzed follows a normal distribution, and the parameters of the population are known or can be estimated. These tests are generally more powerful and can be used with larger sample sizes. Examples of parametric tests include t-tests, ANOVA, and Pearson's correlation.
• Pearson's correlation is a parametric test used to measure the linear relationship between two continuous variables. It assumes that the data is normally distributed and there is a linear relationship between the variables. It produces a coefficient, called the Pearson correlation coefficient, that ranges from -1 to +1, where -1 represents a perfect negative correlation, 0 represents no correlation, and +1 represents a perfect positive correlation.

Non-parametric tests:

• Non-parametric tests, on the other hand, do not make assumptions about the distribution of the data or the parameters of the population. They are often used when the data is not normally distributed, or when the sample size is small. Examples of non-parametric tests include Chi-square test, Spearman's correlation, and Wilcoxon rank-sum test.
• Spearman's correlation is a non-parametric test that measures the monotonic relationship between two variables, and does not assume a normal distribution or a linear relationship.
• Chi-square test is also a non-parametric test, used to analyze the categorical data.
• Sign test is another non-parametric test used to analyze the matched pair data.

Therefore it is clear that Pearson's correlation is a parametric test.

we generally make use of parametric and non-parametric tests for making inferences about various population values (parameters). Many methods and techniques are used in statistics. These have been grouped under parametric and non-parametric statistics.

Hence, For use of a non-parametric test like the chi-square, No assumption about the nature of distribution is required.

Additional Information

Chi-square:

• It's a nonparametric test used to find
  • whether two variables are related to each other or not. (known as a test for independence)
  • whether the sample data matches the population (Known Goodness of FIT test).
• In question, we have more than one independent variable while Chi-square is for only one independent variable.
• E.g. A researcher is conducting a study to know whether educational qualification and socio-economic status are related for people in Mumbai City.