Title 2nd stats ch 06.pdf ✅

Chapter 6 Statistical Inference One and Two Marks Questions With Answers Question 1. What are parameter and statistic?/Define parameter and statistic. Answer: Statistical constants of the population such as Mean (μ), S.D (σ) are called parameter. Ex:- The population has mean = μ, S.D = σ, population proportion P0 Statistical measures computed from the samples such as Mean (x̄), S.D(σ) are called statistic. Ex:- A random sample of size ‘n’ has mean=x̄ and S.D= s, sample proportion p Question 2. Define Statistical Hypothesis Answer: It is a statement or an assertion made regarding the parameters Question 3. What are null and alternative hypothesis Answer: Null Hypothesis is a hypothesis, which is being tested for possible rejection under the assumption that it is true. Denoted by H0 The hypothesis, which is accepted when the null hypothesis is rejected, is called alternative hypothesis. Denoted by H1. Question 4. Define Simple and Composite Hypothesis. Answer: A hypothesis, which completely specifies the parameter of the distribution, is a simple hypothesis. Ex:- H: μ = μ0 (25) is a is a simple hypothesis, H: The population is normally distributed with mean μ = 25 and. σ = 2 A hypothesis, which does not completely specify the parameter of the distribution, is a composite hypothesis. Ex:- H: The population is normally distributed with mean μ = 25
Chapter 6 Statistical Inference Question 5. Define Standard Error Answer: The standard deviation of the sampling distribution of sample statistic is called S.E of statistic Question 6. Give any two uses of Standard Error. Answer: 1. It is used in interval estimation, to write down the confidence intervals. 2. It is used in testing of hypothesis, to test whether the difference between the sample statistic and the population parameter is significant or not. Question 7. Define Type I/Type II Error Answer: Type I Error is taking a wrong decision to reject the null hypothesis when it is actually true. Type II Error is taking a wrong decision to accept the null hypothesis when it is actually not true.3 Question 8. What is the Power of a test. Answer: It is the probability of rejecting the null hypothesis when it is not true. (1 – β ), Here β = P (Type II Error) which is referred as ‘consumers risk Question 9. Define size of a test. Answer: Probability of occurrence of type I Error is called level of significance, denoted by ‘α’. It is also called as Size of the test. Question 10. Define critical Region and Critical value. Answer: The set of all those values of the test statistic, which lead to the rejection of the null hypothesis, is called critical region (ω).
Chapter 6 Statistical Inference The Critical Region is also called as Rejection Region. The value of test statistic, which separates the critical region (ie. rejection region) and . acceptance regions is called the Critical value, denoted by + k or -k or – k1 / + k2 Question 11. Define level of significance, confidence level and confidence co-efficient. Answer: Probability of occurrence of type I Error is called level of significance, denoted by ‘α’ The confidence interval is the interval within which the unknown population parameter is expected to lie. The prob. that the confidence interval contains the parameter is called confidence coefficient. Question 12. Define Point estimation and Interval estimation. Answer: ‘While estimating the unknown parameter, if a specific’value is proposed as an estimate, which is called Point estimation’. ‘While estimating the unknown parameter instead of a specific value, an interval is proposed, which is likely to contain the parameter is called Interval estimation’ Question 13. What is the best estimator of the population mean? Answer: x̄ Question 14. Define sample space and parameter space. Answer: The set of all samples of size ‘n’ that can be drawn from population is called sample space(S) The set of all the admissible values of the population parameters is called parameter space. Question 15. For a S.N.V. test statistic Z, in left tail test the calculated value is (- 2.63) and