Question

2.) Find the 90% confidence interval for estimating ??_d based on these paired data and assuming normality. (Give your answers correct to one decimal place.)

Before	65	63	66	60	47	64
After	37	53	45	30	59	59

Lower Limit:
Upper Limit:

Answer 1

Differences (Before- After): 28, 10, 21, 30, -12, 5 We calculate sample mean and std deviation from given data Sample Mean, d 13.666667 Sample Variance, s2 Sample std dev, s-V82-v/254.666667 s l5.958279 2(d) 82 「(d-d)2 1273.3 - 254.666667 90% CI for Įld using t-dist Sample Mean -d 13.666667 Sample Standard deviations-15.958279 Sample Size-n- 6 Significance level-a1-0.9 0.1 Degrees of freedom for t-distribution, d.f.-n -1-5 Critical Value -ta/2df to.o5,f-5 2.015 (from t-table, two-tails, d.f.-5) Margin of Error = E-ta/2,df × E 2.015 x 6.51494 S d 15.958279 015 x Margin of Error, E 13.127604 Limits of 90% confidence interval are given by: Lower limit-d-E-13.666667-13.127604 ะ 0.539063 ะ 0.539 Upper limit dE 13.66666713.127604 26.794271 26.794 90% confidence interval is: d - (0.539063, 26.794271) E-13.666667 13.127604 90% CI using t-dist: 0.5 くHa < 26.8 Note that exact answer using technology is: (13.6666666666667 15.9582789381144/SQRT (6) *T. INV (1-(1-0.9)/2,6-1 13.6666666666667+15.9582789381144/SQRT (6) T. INV (1-(1-0.9)/2,6-1) 0.5387472254 , 26.7945861079)