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

A Type I error is also known as a ​False positive.

Key Points

• A Type I error means rejecting the null hypothesis when it’s true. It means concluding that results are statistically significant when, in reality, they came about purely by chance or because of unrelated factors.
• In statistics, a Type I error is a false positive conclusion.
• It is called a false-positive conclusion because it happens when the tester validates a statistically significant difference even though there isn't one.
• It occurs when a researcher incorrectly rejects a true null hypothesis.
• The probability of making a type I error is represented by your alpha level (α).

 Additional information

• Type II error means not rejecting the null hypothesis when it’s false.
• A Type II error means failing to conclude there was an effect when there actually was.
• In reality, the study may not have had enough statistical power to detect an effect of a certain size.

The correct answer is n - 1.
Important Points

In the context of hypothesis testing using a paired t-test, the degrees of freedom is calculated as the number of pairs (n) minus 1.

• The paired t-test is used when the samples are dependent; that is, when there is only one sample that has been tested twice (repeated measures) or when there are two samples that have been matched or "paired".
• This is in contrast to an independent two-sample t-test, which is used when the samples are independent of each other.

So, the correct answer is: n - 1
Additional Information

• The paired t-test is used when you have a single sample that has been tested or measured twice under different conditions (repeated measures) or when you have two samples that are related or matched in some way (e.g., before and after measurements on the same individuals).
• When performing a paired t-test, the differences between the paired observations are calculated, and the t-statistic is then calculated based on these differences.
• The degrees of freedom for the t-distribution used in the test are determined by the number of pairs minus 1.
• The rationale behind subtracting 1 from the number of pairs is because using the differences between pairs reduces the effective sample size by 1.
• Since the paired observations are related, they provide less independent information compared to independent samples.

For example, if you have 10 pairs of observations, you would have 10 differences between the paired values. The degrees of freedom for the paired t-test would be 10 - 1 = 9.

• It's important to note that the degrees of freedom affect the critical values used in determining the statistical significance of the t-test.
• As the degrees of freedom decrease, the critical values increase, leading to wider confidence intervals and less statistical power.

Therefore, when conducting a paired t-test, it is crucial to calculate the degrees of freedom correctly to ensure accurate interpretation and appropriate statistical inference.

The correct answer is I, II, and III.

Key Points

• It is a tentative statement that is to be tasted in the future.
• A supposition explanation made on the basis of limited evidence.
• There are two types of hypotheses:
  • Null hypothesis:
    • Null hypothesis states that there is no significant relationship between two variables.
    • This should be rejected during hypothesis testing.
  • Alternate hypothesis:
    • It is also called a research hypothesis.
    • The alternative hypothesis states that there is a significant relationship between the two variables.

Hence, the hypothesis is an intellectual, brilliant, and intelligent guess.

Key Points

Therefore, A ‐ III, B ‐ I , C ‐ IV , D ‐ II is the correct match. 

Important Points

• In twentieth-century philosophy of science, the contrast between "context of discovery" and "context of justification" dominated and defined arguments about discovery.
• The empirical examination of discoveries reveals that discovery processes frequently follow the principle of induction, but this is merely a psychological reality.
• The distinction between the context of discovery and the context of justification is interpreted as a distinction between the process of developing and validating a hypothesis.

In statistical hypothesis testing, the null hypothesis of a test always predicts no effect or no relationship between variables, while the alternative hypothesis states your research prediction of an effect or relationship.

​Power is the probability of rejecting the null hypothesis when, in fact, it is false.

Key Points The concept of Power:

• Power is the probability of rejecting the null hypothesis when, in fact, it is false.
• Power is the probability of making a correct decision (to reject the null hypothesis) when the null hypothesis is false.
• Power is the probability that a test of significance will pick up on an effect that is present.
• Power is the probability that a test of significance will detect a deviation from the null hypothesis, should such a deviation exist.
• Power is the probability of avoiding a Type II error.

Simply put, Power is the probability of not making a Type II error, according to Neil Weiss in Introductory Statistics.

Additional Information

• Demarcations are the marking of the limits or boundaries.
• Normative data is data from a reference population that establishes a baseline distribution for a score or measurement, and against which the score or measurement can be compared.
• A critical region, also known as the rejection region, is a set of values for the test statistic for which the null hypothesis is rejected. i.e. if the observed test statistic is in the critical region then we reject the null hypothesis and accept the alternative hypothesis.

Type II error is the failure to reject a false null hypothesis.

Key Points

• The null hypothesis is a general statement that states that there is no relationship between two phenomenons under consideration or that there is no association between two groups.
• A Type II error means not rejecting the null hypothesis when it’s actually false.
• A Type II error means failing to conclude there was an effect when there actually was.
• In reality, the study may not have had enough statistical power to detect an effect of a certain size.
• Example of Type II error: the test result says you don’t have coronavirus, but you actually do.

Additional Information

• A Type I error means rejecting the null hypothesis when it’s actually true.
• It means concluding that results are statistically significant when, in reality, they came about purely by chance or because of unrelated factors.

Key PointsStatement I: Type I Error refers to the decision to reject the null hypothesis when it is incorrect.

• A type 1 error is also known as a false positive and occurs if an investigator rejects a null hypothesis that is actually true in the population; 
• A type I error occurs during hypothesis testing when a null hypothesis is rejected, even though it is accurate and should not be rejected.
• The null hypothesis assumes no cause and effect relationship between the tested item and the stimuli applied during the test.
• A type I error is "false positive" leading to an incorrect rejection of the null hypothesis.

Hence, this statement is not correct.

Statement II: Sampling error occurs due to the violation of the principle of random sampling.

• A sampling error happens when the sample utilized in the study isn't representative of the full population.
• Sampling errors usually occur, and thus, researchers invariably calculate a margin of error during final results as a statistical practice.
• The principle of simple sampling is that each set of things has an identical probability of being chosen.

Hence, this statement is not correct.

The correct answer is Sea floor spreading hypothesis. Key Points

• Harry Hammond Hess proposed the seafloor spreading hypothesis in 1962, which explained the mechanism behind continental drift.
• This hypothesis suggested that new oceanic crust is formed at mid-ocean ridges and then moves away from the ridge, carrying the continents with it.
• This theory was supported by evidence such as magnetic anomalies in the oceanic crust and the age of oceanic rocks becoming progressively younger towards the mid-ocean ridges.

Additional Information

• According to Alfred Wegener's theory, the continents were formerly part of a single supercontinent called Pangaea, which means "all of earth" in Greek.
  • He proposed that the continents relocated to their present locations when Pangaea broke apart a long time ago.
  • He dubbed continental drift his theory.
• The Gaia hypothesis was proposed by James Lovelock in the 1970s.
  • It suggests that the Earth is a self-regulating system that maintains conditions necessary for life.
• The geographical cycle hypothesis was proposed by William Morris Davis in the late 19th century.
  • He suggested that landforms were shaped by a cycle of erosion, transportation, and deposition.

A hypothesis is a precise, testable statement of what the researchers predict will be the outcome of the study. Hypothesis testing is the process of making a choice between two conflicting hypotheses. 

Key Points

Assertion (A): A research hypothesis (H1), has to be tested with the help of a Null hypothesis called (H0).

• In hypothesis testing, there are two mutually exclusive hypotheses; the Null Hypothesis (H0) and the Alternative Hypothesis (H1). 
• The null hypothesis, H0, is a statistical proposition stating that there is no significant difference between a hypothesized value of a population parameter and its value estimated from a sample drawn from that population.
• The alternative hypothesis, H1 or Ha, is a statistical proposition stating that there is a significant difference between a hypothesized value of a population parameter and its estimated value. When the null hypothesis is tested, a decision is either correct or incorrect.
• The reason to test the null hypothesis is that we think it is wrong. We state what we think is wrong about the null hypothesis in an alternative hypothesis.

Hence it concludes that the assertion is correct.

Reason (R): Tenability of research hypothesis (H1) cannot be directly affirmed.

• The relationship between the research hypothesis (H₁) and the null hypothesis (H₀) is that, if the null hypothesis (H₀) is rejected then the research hypothesis (H₁) is accepted.
• But in the beginning stage, the researcher makes an affirmative statement, as a prediction of the solution that she proposes to test later.
• At the stage of statistical analysis of data, the research hypothesis is converted into a null hypothesis. All statistical tests are the tests for the null hypotheses.
• Rejecting or accepting the null hypothesis asserts that observed differences or relationships may result from chance errors due to the sampling procedure.

Hence it concludes that the reasoning is also correct. 

Therefore, both (A) and (R) are correct and (R) is the correct explanation of (A)

Key Points 

• In hypothesis testing, the p-value is a measure of the evidence against the null hypothesis. It quantifies the probability of obtaining the observed results (or more extreme results) if the null hypothesis is true. In simple terms, it tells us how likely it is to get the observed data if the null hypothesis is correct.
• Typically, in hypothesis testing, we set a significance level (also known as alpha) which is the threshold for determining statistical significance.
• Common significance levels are 5%, 1%, or 0.01%. If the p-value is less than or equal to the chosen significance level, we reject the null hypothesis, indicating that the observed results are unlikely to occur by chance alone.
• If the p-value is greater than the significance level, we fail to reject the null hypothesis, suggesting that the observed results could reasonably occur due to random chance.

The p-values given in the question:

• B. 32%:
  • Here, the p-value is 32%. If we have set the significance level at 5% (for example), the p-value of 32% is greater than the significance level.
  • Therefore, we fail to reject the null hypothesis, meaning that the evidence against the null hypothesis is not strong enough to consider it false.
• D. 0.42:
  • ​ In this case, the p-value is 0.42. If the significance level is set at 2% (as mentioned in the question), the p-value of 0.42 is greater than the significance level.
  • Again, we fail to reject the null hypothesis, indicating that the evidence against the null hypothesis is not significant.

So, both for p-value 32% and p-value 0.42, the null hypothesis is likely to be accepted, as the evidence against it is not strong enough to support its rejection.