PROBLEM : Take-Home Pay. Are the wages of the two sets of people statistically e
ID: 3223567 • Letter: P
Question
PROBLEM :
Take-Home Pay. Are the wages of the two sets of people statistically equal?
Married
Not Married
$639.60
$658.20
s
$60
$90
n
40
60
Test at a = .02
PROBLEM :
Does smoking makes a difference when it comes to the number of absent days?
Test at .05 significance level.
Smokers: Average number of days absent = 14.7; standard deviation = 5.0; n = 44
Non-Smokers: Average number of days absent = 8.3; standard deviation = 4.0; n = 60
Married
Not Married
$639.60
$658.20
s
$60
$90
n
40
60
Explanation / Answer
PROBLEM :
Take-Home Pay. Are the wages of the two sets of people statistically equal?
Married
Not Married
$639.60
$658.20
s
$60
$90
n
40
60
Test at a = .02
Answer :
Null Hypothesis : There is no difference between wages of married and unmarried people.
married= unmarried
Alternative Hypothesis : There is significant difference between wages of married and unmarried people. married unmarried
Test Statistic:
first we have to calculate spooled = sqrt [ {(n1-1) s12+ ( n2-1) s22}/ (n1+ n2-2) ]
= sqrt [ (39 * 602 + 59 * 902 )/(40 + 60 -2)] = 79.43
and Standard error of estimate SE= spsqrt [ 1/n1+ 1/n2] = 79.43 * sqrt [ 1/40 + 1/60] = 16.2135
Test Statistic:
t = ( xmarried- Xunmarried)/ SE = (658.20 - 639.60)/ 16.135 = 1.1527
tcriticalfor dF = 98 and alpha = 0.02
tcritical = 2.365
so here t < tcritical so we cannot reject the null hypothesis and can conclude that there is no significant difference between mean values of wages for married and unmarried people.
PROBLEM :
Does smoking makes a difference when it comes to the number of absent days?
Test at .05 significance level.
Smokers: Average number of days absent = 14.7; standard deviation = 5.0; n = 44
Non-Smokers: Average number of days absent = 8.3; standard deviation = 4.0; n = 60
Answer :
Null HYpothesis : There is no difference between average number of days absent among smokers and non - smokers. smokers= non-smokers
Alternative Hypothesis : There is statistically significant difference between average number of days absent among sokers and non - smokers. smokers non-smokers
Test Statistic:
first we have to calculate spooled = sqrt [ {(n1-1) s12+ ( n2-1) s22}/ (n1+ n2-2) ]
= sqrt [ (43 * 52 + 59 * 42 )/(44 + 60 -2)] = 4.449
and Standard error of estimate SE= spsqrt [ 1/n1+ 1/n2] = 4.449 * sqrt [ 1/44 + 1/60] = 0.8830
Test Statistic:
t = ( xmarried- Xunmarried)/ SE = (14.7 - 8.3)/ 0.8830= 7.248
tcriticalfor dF = 102 and alpha = 0.05
tcritical = 1.9835
so here t < tcritical so we can reject the null hypothesis and can conclude that there is significant difference between mean values of number of days absent between smokers and non sokers.
Married
Not Married
$639.60
$658.20
s
$60
$90
n
40
60
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