Question
When Ho is rejected and infact it is true, the researcher is committing a :
The correct answer is
Type I error
In hypothesis testing, two types of errors can occur when making a decision about the null hypothesis ($H_0$). Understanding these errors is crucial for interpreting research results correctly.
Hypothesis Testing Error Identification
The question describes a scenario where the null hypothesis ($H_0$) is actually true, but the researcher decides to reject it. This specific situation corresponds to a well-defined statistical error.
Defining Statistical Errors
- Type I error: This occurs when a true null hypothesis ($H_0$) is rejected. The probability of making a Type I error is denoted by $\alpha$ (alpha), often referred to as the significance level.
- Type II error: This occurs when a false null hypothesis ($H_0$) is not rejected (i.e., failing to reject $H_0$ when it is false). The probability of making a Type II error is denoted by $\beta$ (beta).
Conclusion on Researcher's Action
When the null hypothesis ($H_0$) is true and is rejected by the researcher, it perfectly matches the definition of a Type I error. Therefore, the researcher is committing a Type I error.
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Important Questions from Hypothesis testing
- Assertion (A) : When sample size is small and/or data are badly skewed (so that assumption of normality is doubtful) parametric methods are not applicable.
Reason (R) : In parametric tests we can assume that scores upon which our statistics are based are normally distributed in the population.
Code : - Arrange in order the steps in testing for statistical significance :
(i) Select the statistical test to be applied
(ii) State the research question
(iii) Compute the test statistic
(iv) State the null and alternate hypothesis
(v) Compare the test statistic with the critical value
(vi) Interpret the results.
Code : - Assertion (A) : Assumption free tests are some what less powerful than parametric techniques when assumption for the latter are met.
Reason (R) : Assumption free tests are less powerful because the researchers do not use scientific sampling methods.
Code : - Arrange in order the steps in hypothesis testing about a single population mean using the normal curve model :
(a) Decide of n and draw a random sample
(b) Reject/retain Ho on basis of z calculated
(c) Calculate $\bar{\text{x}}$ and $\sigma_{\bar{\text{x}}}$
(d) Identify $\alpha$ level
(e) Define the target population
(f) Specify Ho and HA
(g) Calculate z-score
Code : - Type-I error in drawing statistical inference while testing the null hypothesis is
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