Research MCQ Quiz in मल्याळम - Objective Question with Answer for Research - സൗജന്യ PDF ഡൗൺലോഡ് ചെയ്യുക

Standard deviation refers to how much the values are spread out from a given set of values. It is a measure of how far each observed values are from the mean.

A confidence interval for normal distributions is an interval within which we expect the actual outcome to fall with a given probability.

The four commonly used confidence intervals for a normal distribution are:

• 68.27% of values fall within 1 standard deviation of the mean (-1s <= X <= 1s)
• 90% of values fall within 1.65 standard deviations of the mean (-1.65s <= X <= 1.65s)
• 95% of values fall within 1.96 standard deviations of the mean (-1.96s <= X <= 1.96s)
• 99.73% of values fall within 2.58 standard deviations of the mean (-2.58s <= X <= 2.58s)

The confidence level is represented as, where 'n' is the number of observations.

For example, n = 1.96 for 95% confidence level.

Therefore, the total area of a normal distribution between the average value ± 1.96 of standard deviation is 95%.

Standard Deviation formula:

\(\sigma = \sqrt {\frac {\sum (x_i - \mu)^2}{N}}\)

Where, 

= population standard deviation,  = the size of population,  = each value from population,  = the population mean.

The correct answer is the U test.

Key Points

For testing the significance of the difference between the two sample means, which of the following test is used t-test.

Key Points

"t" test: 

• It is used to compare the means of two groups.
• It is used in hypothesis testing to find out whether a process actually has an effect on the population, or whether the groups are different from one another.
• A test is necessary for small sample sizes (n<30) where distributions are not normal.

Additional Information

"F" test:

• F-test is any statistical test in which the test statistic has an F-distribution under the null hypothesis.
• The parameters used in the f-test are mean and variances due to which parametric tests are used here as well.
• F-test of overall significance indicates whether your linear regression model provides a better fit to the data than a model that contains no independent variables.
• F-test uses two sample variances, s1 and s2, by dividing them.
• There result is always a positive number because variances are always positive.

x2 "Chi-square" test:

• It is a statistical hypothesis test that compares two variables of a contingency test to check how they are related.
• It is a nonparametric test and this test normally applies to qualitative data.
• There are two types of chi-square test:

1. Chi-square goodness of fit test that determines if sample data matches with the population.
2. A chi-square test for independence tests to see whether the distribution of categorical variables differs from each other. 

"z" test:

• This statistical technique is used to determine whether two populations are different from each other when variances are known and to calculate their mean.
• This test can be used to test the hypothesis that follows a normal distribution.
• When the sample size of the population is greater than equal to 30 i.e. n>=30 then a z-test will be used.

Parametric tests:

• A statistical test, in which specific assumptions are made about the population parameter is known as a parametric test.
• Parametric tests make certain assumptions about a data set; namely that the data are drawn from a population with a normal distribution.
• This test is only used where a normal distribution is assumed.
• The most widely used parametric tests are the t-test (paired or unpaired), ANOVA (one-way non-repeated, repeated; two-way, three-way), linear regression, and Pearson rank correlation. 
• Parametric tests in general are more powerful (require a smaller sample size) than nonparametric tests.
• A parametric test is preferred because it has a better ability to distinguish between the two arms.
• In other words, it is better at distinguishing the weirdness of the distribution.
• Nonparametric tests are only about 95% as powerful as parametric tests.

Therefore, (A) is correct and (B) is incorrect.

Formula: \(SE_\bar X\) = σ / √n

Therefore, √n = σ / \(SE_\bar X\)

                  √n = 40 / 8

                  √n = 5

                   n = 25

Therefore, For a very large population the ratio between \(SE_\bar X\) and σ is 8 : 40. The sample size n will be 25

The correct answer is the underlying distribution.

Key Points

Parametric tests are used in studying the characteristics of the population. It is used in making certain assumptions about the population.

Important Points 

Parametric tests:

Parametric tests are those tests in statistics that are used in making assumptions about the parameters of population distribution. Through these tests, one can make assumptions about the characteristics of the distribution of a population. Some examples of parametric tests are the t-test, f-test, and z-test. In these types of tests, the test measurement of variables is done on an interval or ratio scale. The measurement of central tendency in these tests is mean.

Non Parametric tests: 

These tests are distribution-free and are used for non-normal variables. These tests are used when a researcher has no information about the population. Some of the examples of nonparametric tests are Chi-square tests and U-tests. These tests evaluate the hypothesis for the whole population. Here median is taken as a measure of central tendency. These tests can be applied for both variables and attributes. Hence, the correct answer is the underlying distribution.

The correct answer is B, D, C, A, E.

Key PointsThe correct steps in sequence for testing a statistical hypothesis are as follows:

• Framing the hypothesis: The first step necessitates setting a null and an alternative hypothesis to establish the grounds of the statistical test.
• Level of significance: In the next step, we decide the level of significance we're going to use. Commonly, it's 0.05 or 5%, but it can vary depending on the nature of the research. This level represents the likelihood that the difference in the sample findings occurred by chance.
• Collecting the sample data: After establishing the hypothesis and level of significance, we collect the data that we are going to test. This could involve conducting surveys, carrying out experiments, observing phenomena, etc.
• Test statistics: When we have the data on hand, we run the analysis and calculate the test statistic (such as t value, z score etc.) that will determine whether or not we reject the null hypothesis.
• Obtaining results and taking decisions: Finally, we compare our test statistic to the critical values associated with our level of significance. Depending on the outcome, we then decide whether to reject or retain the null hypothesis.

Key Points

• Review of literature
  • The review of literature involves the systematic analysis of existing research to identify gaps, trends, and key findings.
  • It helps researchers to avoid reinventing the wheel by building upon previous work instead of duplicating it.
  • By studying earlier research, scholars can focus on unexplored areas or refine methodologies to achieve better outcomes.
  • It ensures that the current research is placed in the context of existing knowledge, providing a strong foundation for formulating objectives and hypotheses.

Additional Information

• Key components of a literature review
  • Identification of relevant sources: Books, journal articles, conference proceedings, and credible online resources.
  • Categorization of information: Grouping studies by themes, methodologies, or findings.
  • Critical evaluation: Assessing the reliability, validity, and relevance of the studies reviewed.
• Benefits of a literature review
  • Facilitates better understanding of the research topic by providing a comprehensive overview of existing work.
  • Helps in identifying research gaps that can be explored in the current study.
  • Provides contextual support for justifying the need for the research.
• Other related concepts
  • Sampling: The process of selecting a subset of a population for analysis, distinct from reviewing existing literature.
  • Objectives of the study: These are specific goals derived from the literature review and define what the research aims to achieve.
  • Hypothesis of the study: A testable prediction derived from the literature review, forming the basis of the research investigation.

The correct answer is Content Validity

Key Points Content Validity:

A test that is content valid is one that contains a fair sample of the tasks and skills actually needed for the job in question.

Example : Selecting students for dental school, many schools give applicants chunks of chalk, and ask them to carve something that looks like a tooth. If the content you choose for the test is a representative sample, then the test is content valid. 

Additional Information Construct validity: Construct validity refers to how well the measure 'behaves' in accordance with theoretical hypotheses, and it measures how well the instrument's results reflect the theoretical construct.

Test validity: The degree to which a test (such as a chemical, physical, or scholastic test) accurately measures what it is designed to assess is known as test validity.

Criterion validity: A measure's criterion validity is an estimate of how well it agrees with a gold standard (i.e., an external criterion of the phenomenon being measured). The lack of gold standards in criterion validity assessment for questionnaire-based measures is a key issue.

The correct answer is 30

Important Points Solution:

∑ (x – 20) denotes that 20 is subtracted from each observation

Total observation = 10

Therefore, total amount subtracted from all observation = 20 x 10 = 200

Hence,

∑ x - 200 = 100

∑ x = 100 + 200

∑ x = 300

Arithmetic Mean = Sum of Observation / Number of Observation

Arithmetic Mean = 300 / 10

Arithmetic Mean = 30