A study was conducted among individuals with chronic pain to

A study was conducted among individuals with chronic pain to determine how eective 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% condence 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% condence interval for the mean sensory rate? (Round your answer to the nearest 2 decimal places)
(f) Calculate the 95% condence interval for the mean sensory rate.

i. What is the value of the lower bound of the 95% condence interval? (Round your answer to the nearest 2 decimal places)

ii. What is the value of the upper bound of the 95% condence interval? (Round your answer to the nearest 2 decimal places)
(g) [Free Response] Interpret the condence interval you constructed above in the context of the problem.
(h) Assume that the standard deviation of all the sensory rates is known to be 1.67. Calculate the 95% condence interval for the mean sensory rate under this situation. i. What is the value of the lower bound of the 95% condence interval? (Round your answer to the nearest 2 decimal places) ii. What is the value of the upper bound of the 95% condence interval? (Round your answer to the nearest 2 decimal places)
(i) [Free Response] Is the 95% condence interval constructed in part(f) wider or narrower than the 95% condence interval in part(h)? Explain why.

Solution