please explain all steps A researcher is interested in knowing how friendship mi
ID: 3232358 • Letter: P
Question
please explain all steps
A researcher is interested in knowing how friendship might affect sales such as laptop shopping. For this purpose, she randomly surveyed two groups of students and asked them how much they would be willing to pay for a used laptop i) When buying from a friend, ii) When buying from a stranger. The following are the prices they offered. a) Assuming that the variances of the two groups are equal, what is a 95% Confidence Interval for the difference of the means of the two groups of students? b) What does this confidence interval suggest in terms of the amount of money people offer to friends and strangers, i.e., in which case do they offer more?Explanation / Answer
(a)
n1 = 8
n2 = 7
x1-bar = 281.88
x2-bar = 211.43
s1 = 18.31
s2 = 46.43
% = 95
Degrees of freedom = n1 + n2 - 2 = 8 + 7 -2 = 13
Pooled s = (((n1 - 1) * s1^2 + (n2 - 1) * s2^2)/DOF) = (((8 - 1) * 18.31^2 + ( 7 - 1) * 46.43^2)/(8 + 7 -2)) = 34.2852986
SE = Pooled s * ((1/n1) + (1/n2)) = 34.2852985986705 * ((1/8) + (1/7)) = 17.74432782
t- score = 2.160368652
Width of the confidence interval = t * SE = 2.16036865224853 * 17.7443278160334 = 38.33428957
Lower Limit of the confidence interval = (x1-bar - x2-bar) - width = 70.45 - 38.3342895689803 = 32.11571043
Upper Limit of the confidence interval = (x1-bar - x2-bar) + width = 70.45 + 38.3342895689803 = 108.7842896
The 95% confidence interval is [$32.12, $108.78]
(b) Since the entire confidence interval is positive, it means people usually end up paying more when they buy from friends.
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