**Exercise: T-Distribution and Degrees of Freedom****Problem 16:**Given a sample size of \( n = 83 \), find \( P(t < -0.46) \).**Hint:**Use the closest degree of freedom. Since the table only provides positive \( t \) values, you should look up \( t = 0.46 \).**Table Explanation:**The table shows the critical \( t \)-values for different degrees of freedom (df) at various significance levels. The highlighted column corresponds to a degree of freedom \( df = 80 \).- Values for one-sided and two-sided tests are provided at common significance levels (e.g., 0.05, 0.01). - \( df \) are listed vertically on the left, ranging from 40 to 1000 or more. #### Options for Solution:a. \( 0.1 < P(t < -0.46) < 0.15 \)b. \( 0.15 < P(t < -0.46) < 0.2 \)c. \( P(t < -0.46) > 0.25 \)d. \( P(t < -0.46) < 0.0025 \)**Problem 17:**With a sample size of \( n = 5 \), determine the range where \( P(t < -1.7) \) is bounded.a. \( 0.05, 0.1 \)b. \( 0.01, 0.15 \)c. \( 0.15, 0.2 \)d. \( 0.2, 0.25 \)**Problem 18:**For a sample size of \( n = 1000 \), find the range for \( P(t < -1.7) \).a. \( 0.025, 0.05 \)b. \( 0.05, 0.1 \)c. \( 0.1, 0.15 \)d. \( 0.15, 0.2 \)**Discussion: Comparing t Distributions with the z Distribution**The following questions illustrate the interpretation of degrees of freedom \( (df) \) and critical values for different sample sizes. Reference: **Chapter 17 Section - "The t distributions"** (p413)

Name: **Exercise: T-Distribution and Degrees of Freedom****Problem 16:**Giv
Uploaded: 2024-03-20T07:07:12.000Z
Channel: Bartleby
Description: **Exercise: T-Distribution and Degrees of Freedom****Problem 16:**Given a sample size of \( n = 83 \), find \( P(t < -0.46) \).**Hint:**Use the closest degree of freedom. Since the table only provides positive \( t \) values, you should look up \( t