F 3 **Question 3**The sampling distribution used when making inferences about a single population's variance is:- a. an F distribution.- b. a t distribution.- c. a chi-square distribution.- d. a normal distribution.**Question 4**Which of the following has a chi-square distribution?- a. \((n - 1)s^2/\sigma^2\)- b. \((n - 1)\sigma/s\)- c. \((n - 1)s/\sigma\)- d. \((n - 1)s^2/\sigma^2\)Note: In Question 4, option a and option d appear to be identical. Please verify if there's a typographical error.

Q.3: The sampling distribution used when making inferences about a single population's variance is a chi-square distribution (option 'c') Explanation: To test the single population Variance to compare it to specific Variance we have to use the chi-square test Statistic at (n-1) degrees of freedom. Assumptions : i)The sample must be random. ii)The underlying distribution is Normal. χ2 test statistic = (n-1)*s2/σ2 n = the total number of observations in the sample data s2 = sample variance σ2 = hypothesized value of the population variance Decision Rule : Reject Ho null hypothesis when test Statistic falls in the critical region. This is the hypothesis test for testing one population Variance Q.4 Answer: A Chi-square (χ2) distribution= (n-1)*s2/σ2