. Find the critical values (“z”, "??"?? “t” scores) for the following.a. C.L. = 98%, n is 25 and σ is unknown.b. Alpha is 3%, the sample size is 45 and sigma is known.d. α is .5%, n=15;sigma is known for the left tail (not “z”)e. 90%, chi-square right, when the sample size is 22.( ???) **Formulas**1. \( x^2_R(df, \alpha) \) 2. \( x^2_L(df, 1-\alpha) \) 3. \( \frac{(n-1)s^2}{x^2_R} \leq \sigma^2 \leq \frac{(n-1)s^2}{x^2_L} \) 4. \( x^2_R(df, \alpha/2) \) 5. \( x^2_L(df, 1-\alpha/2) \) 6. \( x^2_L(df, 1-\alpha) \) 7. \( \sqrt{\frac{(n-1)s^2}{x^2_R}} \leq \sigma \leq \sqrt{\frac{(n-1)s^2}{x^2_L}} \) **Explanation of Variables:**- \( df \) = degrees of freedom- \( \alpha \) = significance level- \( n \) = sample size- \( s^2 \) = sample variance- \( \sigma^2 \) = population variance- \( \sigma \) = population standard deviation- \( x^2_R \) and \( x^2_L \) = Chi-square distribution values for right and left tails respectivelyThese formulas are essential for calculating confidence intervals and conducting hypothesis tests involving variances and standard deviations.

a) We use the student's t-test at (n-1)=24d.f. as population s.d. is unknown and n<30 b) Since, n>30, We use the z-test statistic for α=0.03(d) Given: α=0.005n=15 Since, n<30, th study is on students' t-distribution with (n-1) d.f. The critical values are points at the tail(s) of a specific distribution, with the property that the area under the curve for those critical points in the tails is equal to the given value of \alphaα The distribution in this case is the Student's t distribution. In general terms, for a two-tailed case, the critical values correspond to two points to the left and right of the center of the distribution, that have the property that the sum of the area under the curve for the left tail (from the left critical point) and the area under the curve for the right tail is equal to the given significance level \alphaα. For a left-tailed case, the critical value corresponds to the point to the left of the centre of the distribution, with the property that the area under the curve for the left tail (from the critical point to the left) is equal to the given significance level \alphaα. Since you have posted a question with multiple subparts, we will solve the first 3 subparts for you. To get the remaining subpart done please repost the -–- question and mention the subparts to be solved.