Question 3Answer Part D and Interpretation Only!! The image displays a t-Distribution table, which provides critical t-values for various degrees of freedom (df) and tail areas. This table is used in statistics to determine the critical value of the t-distribution at a given significance level, particularly in hypothesis testing.### Table Details:- **df (Degrees of Freedom):** The first and last columns represent the degrees of freedom, ranging from 1 to 1000. - **Columns for Areas in the Right Tail:** The top row lists probabilities or tail areas: 0.25, 0.20, 0.15, 0.10, 0.05, 0.025, 0.02, 0.01, 0.005, 0.0025, 0.001, 0.0005. - **Values in the Table:** Each cell within the table corresponds to a critical t-value, which is used to determine the boundary at which the t-distribution's cumulative probability equals the specified areas in the right tail for the corresponding degrees of freedom.For example, for a degree of freedom (df) of 10 and an area of 0.05 in the right tail, the critical t-value is 1.812 (from the 6th degree of freedom row, under the 0.05 column).This table is essential for performing t-tests, especially when determining confidence intervals and hypothesis testing for small sample sizes in statistical analyses. To test \( H_0: \mu = 107 \) versus \( H_1: \mu \neq 107 \), a simple random sample of size \( n = 35 \) is obtained. Complete parts a through e below.- **[Instruction to view t-Distribution Area in Right Tail]**### (a) - **Options:** - C. Yes, because \( n \geq 30 \). - D. No, because the test is two-tailed.### (b) If \( \bar{x} = 103.8 \) and \( s = 5.9 \), compute the test statistic.The test statistic is \( t_0 = -3.21 \). (Round to two decimal places as needed.)### (c) Draw a t-distribution with the area that represents the P-value shaded. Choose the correct graph below.- **Middle Graph**: A t-distribution with shading in both tails indicating a two-tailed test.### (d) Approximate the P-value. Choose the correct answer below.- **Options:** - A. \( 0.005 < P\text{-value} < 0.01 \) - B. \( 0.01 < P\text{-value} < 0.02 \) - C. \( 0.002 < P\text{-value} < 0.005 \) - D. \( 0.001 < P\text{-value} < 0.002 \)### Interpret the P-value. Choose the correct answer below.- **Options:** - A. If 1000 random samples of size \( n = 35 \) are obtained, about 3 samples are expected to result in a mean as extreme or more extreme than the one observed if \( \mu = 103.8 \). - B. If 1000 random samples of size \( n = 35 \) are obtained, about 3 samples are expected to result in a mean as extreme or more extreme than the one observed if \( \mu = 107 \). - C. If 100 random samples of size \( n = 35 \) are obtained, about 3 samples are expected to result in a mean as extreme or more extreme than the one observed if \( \mu = 107 \). - D. If 100

d) The sample size n is 35.The degrees of freedom is n-1=35-1=34. The p-value for the test statistic of -3.21 using student t table or Excel function “=t.dist.2t(3.21,34)” is 0.0029. Thus, the p-value lies between 0.002<P-value<0.005. The interpretation is B) if 1000 random samples of size n= 35 are obtained, about 3 sample are expected to result in a mean as extreme or more extreme than one observed if µ =107.