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home / study / questions and answers / math / statistics and probability / confidence level unknown (t 2 ,n1) ) ... Question Confidence Level unknown (t 2 ,n1) ) df = 6 df = 30 df = 100 known (z 2 ) 80% 90% 95% 99% Accurate to the nearest 3 decimal places, what is the critical value (t 2 ,n1 or z 2 ) that corresponds to the given confidence levels and degrees of freedom. Fill in the following table with the appropriate critical values: (c) A 90% confidence interval using df = 6 is based on how many observations? (d) A 95% confidence interval using df = 30 is based on how many observations? (e) [Don’t forget how to use Table A] What is the positive value of z 2 for a 74% confidence interval when is known? 2. Probabilities from the t-table (Table D). Notice that some of the questions below use df and some use n. What is the value of (a) P(T 3.421) for df = 27? [up to the nearest 3 decimal places] (d) P(T > 3.421) for n = 28? [up to the nearest 3 decimal places] (e) P(T 1.363) for df = 11? [up to the nearest 1 decimal place 3. Answer the following questions on-line by checking either True or False. (a) The t-distribution is characterized by the parameters µ (the mean) and (the standard deviation). (b) The t-table (Table D) works with the area above (right or upper tail) while the z-table (Table A) works with the area below (left or lower tail). (c) The t-distribution approaches the Standard Normal Distribution, N(0, 1), as the degrees of freedom increase because s estimates with less precision when the sample size increases. 4. A study was conducted among individuals with chronic pain to determine how effective acupuncture is in relieving pain. A random sample of 15 subjects were chosen and their sensory rates were measured. Assume that the measurements on sensory rates follow a normal distribution. The data from the study are given below: 8.6 9.4 7.9 6.8 8.3 7.3 9.2 9.6 8.7 11.4 10.3 5.4 8.1 5.5 6.9 (a) What is the value of ¯x, the sample mean (Use JMP or MS Excel to calculate)? (Round your answer to the nearest 2 decimal places) (b) What is the value of s, the sample standard deviation (Use JMP or MS Excel to calculate)? (Round your answer to the nearest 2 decimal places) (c) Report the degrees of freedom associated with the t-distribution. (d) What is the value of t 2 ,n1 for the 95% confidence interval for the mean sensory rate? (The value obtained from Table-D, accurate to the nearest 3 decimal places) (e) What is the margin of error for the 95% confidence interval for the mean sensory rate? (Round your answer to the nearest 2 decimal places) (f) Calculate the 95% confidence interval for the mean sensory rate. i. What is the value of the lower bound of the 95% confidence interval? (Round your answer to the nearest 2 decimal places) ii. What is the value of the upper bound of the 95% confidence interval? (Round your answer to the nearest 2 decimal places) (h) Assume that the standard deviation of all the sensory rates is known to be 1.67. Calculate the 95% confidence interval for the mean sensory rate under this situation. i. What is the value of the lower bound of the 95% confidence interval? (Round your answer to the nearest 2 decimal places) ii. What is the value of the upper bound of the 95% confidence interval? (Round your answer to the nearest 2 decimal places)

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