show all work. No credit given for an ansW ots) The following data shows data on

Question

show all work. No credit given for an ansW ots) The following data shows data on oxidation-induction time (min) for various nmercial oils. Assuming that the oxidation-induction time is normally distributed. 87 103 142 132 211 105 99 (4) Construct a 95 percent two-sided confidence interval on the mean range (the ? is not known yet) . b. (4) Construct a 97.5 percent lower-confidence bound on the mean range (still the ?is not known yet). (5) Assuming that the population standard deviation of the time ?= 50, what sample size is necessary to ensure that the resulting 95% CI has a width of (at most) 50? C. 2

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 95% = 2.9687

CI = mean +/- t *(s/sqrt(n))
= 125.5714 +/- 2.9687 *(42.2999/sqrt(7))
= (78.1085 , 173.0343 )

c)

ME = 50 , s = 50
t value at 95% = 2.447

ME = t *(s/sqrt(n))
50 = 2.447 *(50/sqrt(n))

n = 6

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