Please explain as much as possible and show calculations. Thanks in advance! sho
ID: 3370228 • Letter: P
Question
Please explain as much as possible and show calculations. Thanks in advance!
show all work. No credit given for ull ots) The following data shows data on oxidation-induction time (min) for various mmerci ial oils. Assuming that the oxidation-induction time is normally distributed. 87 103 142 132 211 105 99 a (4) Construct a 95 percent two-sided confidence interval on the mean range (the o is not b, (4) Construct a 97.5 percent lower-confidence bound on the mean range (still the ?is not C. (5) Assuming that the population standard deviation of the time ? 50, what sample size known yet). known yet). is necessary to ensure that the resulting 95% CI has a width of (at most) 50?Explanation / Answer
a)
mean = 125.5714 ,std.dev = 42.2999 , n = 7
t value at 95% = 2.447
CI = mean +/- t *(s/sqrt(n))
= 125.5714 +/- 2.447 *(42.2999/sqrt(7))
= (86.4505 , 164.6923 )
b)
mean = 125.5714 ,std.dev = 42.2999 , n = 7
t value at 97.5% = 2.447
CI = mean - t *(s/sqrt(n))
= 125.5714 - 2.447 *(42.2999/sqrt(7))
= (86.4505, infinite)
c)
ME = 50/2 = 25 , s = 50
z value at 95% = 1.96
n = (z*sigma/ME)^2
n = (1.96*50/25)^2
n = 15