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III. Practice Exercises: Read the following problems carefully. Analyze and solve systematically. 1. Suppose you have a sample of size = 12 from a normal distribution. Find the critical value that corresponds to a 95% confidence level.

III. Practice Exercises: Read the following problems carefully. Analyze and solve systematically. 1. Suppose you have a sample of size = 12 from a normal distribution. Find the critical value that corresponds to a 95% confidence level.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Please refer to the lesson (sketch also the normal curve)
III. Practice Exercises: Read the following problems carefully. Analyze and solve systematically. 1. Suppose you have a sample of size = 12 from a normal distribution. Find the critical value that corresponds to a 95% confidence level. 2. For a t - distribution with degrees of freedom = 27, find the value of such that the unshadedarea to the right of - is 0.90. 3. A student suspects that the 16 data she collected for research study do not represent the target population. The data she collected represents a mean of 29 and standard deviation of 8. the population mean is 27. Assuming normality in the target population, is the student's suspicion correct? Use a 90% confidence level.
Transcribed Image Text:III. Practice Exercises: Read the following problems carefully. Analyze and solve systematically. 1. Suppose you have a sample of size = 12 from a normal distribution. Find the critical value that corresponds to a 95% confidence level. 2. For a t - distribution with degrees of freedom = 27, find the value of such that the unshadedarea to the right of - is 0.90. 3. A student suspects that the 16 data she collected for research study do not represent the target population. The data she collected represents a mean of 29 and standard deviation of 8. the population mean is 27. Assuming normality in the target population, is the student's suspicion correct? Use a 90% confidence level.
II. Learning Activity: The t-distribution, just like the z-distribution or standard normal curve, is bell-shaped and unimodal. It is symmetric about = 0. However, it is flatter in the middle and has more area in its tail than that of the standard normal curve. Its shape depends on the sample size . As the sample size becomes larger, the t - distribution gets closer to the standard normal distribution. Flatter V Wider area of tails standardi normal curve t-distribution curve The t-distribution is used with small samples taken from population that is approximately normal. The z - statistic is used when ≥ 30 while t - statistic is used when <30. The t - statistic below uses the sample deviation especially when the population variance is unknown. #U The t - distribution formula is: = where: - sample mean -population mean - sample size - standard deviation of the sample mean Example # 1 A sample of size = 20 is a random sample selected from a normally distributed population. Find the value of such that the shaded area to the left of - is 0.05 Solution: Find the degree of freedom 0. 0.05 0.05 y one-tail/= 0.50 0.25 0.20 0.05 two-tails / a 1.00 0.50 0.40 0.10 df 1 0.000 1.000 1.376 6.314 2 0.000 0.816 1.061 2.920 3 0.000 0.765 0.978 2.353 *** www 19 0.000 0.688 0.861 1.729 20 0.000 0.687 0.860 1.725 A portion of the t - table Since the distribution is symmetric about 0, then the area to the right of is 0.05 also. In the Table of t- Critical Values, move down the first column headed df until = 19. Move to the right until the column headed 0.05 (area in one-tail) or 0.10 (area in two-tails). Therefore, D.=0.000 with 00 = 00. Example # 2 For a t-distribution with 27 degrees of freedom, find the value of such that the area between - and is 0.90. Solution: a. The degree of freedom = 27. b. (1)100% = 90% (1)1 = 0.90 0.90 = 0.10 (two-tails) == 0.05 (one-tail) -t t In the Table of t-Critical Values, move down the first column headed df until = 27. Move to the right until the column headed 0.05 (area in one-tail) or 0.10 (area in two-tails). Hence, D.00 = 0.000 with DD = 00. 1-0 =00 00=20-1 □□ = 19 NO -t t
Transcribed Image Text:II. Learning Activity: The t-distribution, just like the z-distribution or standard normal curve, is bell-shaped and unimodal. It is symmetric about = 0. However, it is flatter in the middle and has more area in its tail than that of the standard normal curve. Its shape depends on the sample size . As the sample size becomes larger, the t - distribution gets closer to the standard normal distribution. Flatter V Wider area of tails standardi normal curve t-distribution curve The t-distribution is used with small samples taken from population that is approximately normal. The z - statistic is used when ≥ 30 while t - statistic is used when <30. The t - statistic below uses the sample deviation especially when the population variance is unknown. #U The t - distribution formula is: = where: - sample mean -population mean - sample size - standard deviation of the sample mean Example # 1 A sample of size = 20 is a random sample selected from a normally distributed population. Find the value of such that the shaded area to the left of - is 0.05 Solution: Find the degree of freedom 0. 0.05 0.05 y one-tail/= 0.50 0.25 0.20 0.05 two-tails / a 1.00 0.50 0.40 0.10 df 1 0.000 1.000 1.376 6.314 2 0.000 0.816 1.061 2.920 3 0.000 0.765 0.978 2.353 *** www 19 0.000 0.688 0.861 1.729 20 0.000 0.687 0.860 1.725 A portion of the t - table Since the distribution is symmetric about 0, then the area to the right of is 0.05 also. In the Table of t- Critical Values, move down the first column headed df until = 19. Move to the right until the column headed 0.05 (area in one-tail) or 0.10 (area in two-tails). Therefore, D.=0.000 with 00 = 00. Example # 2 For a t-distribution with 27 degrees of freedom, find the value of such that the area between - and is 0.90. Solution: a. The degree of freedom = 27. b. (1)100% = 90% (1)1 = 0.90 0.90 = 0.10 (two-tails) == 0.05 (one-tail) -t t In the Table of t-Critical Values, move down the first column headed df until = 27. Move to the right until the column headed 0.05 (area in one-tail) or 0.10 (area in two-tails). Hence, D.00 = 0.000 with DD = 00. 1-0 =00 00=20-1 □□ = 19 NO -t t
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