**Table At Bottom** A research study examined the differences between older and
ID: 2928528 • Letter: #
Question
**Table At Bottom** A research study examined the differences between older and younger adults on perceived life satisfaction. Ten older adults over the age of 70 and ten younger adults between 20 and 30 took a life satisfaction test. Scores on the measure range from 0 to 60, with high scores indicative of high life satisfaction and low scores indicative of low life satisfaction. The data obtained are shown below. If µX and µY are the population means for life satisfaction scores in older and younger adults respectively, and 2 is the population variance (the same in both populations), a. Compute unbiased estimates for µX, µY and 2 from this data. b. You want to test whether older adults have a higher life satisfaction score than younger adults. State the null hypothesis H0 and the alternate hypothesis H1. c. Compute the t-statistic and the number of degrees of freedom. d. What is the likelihood that the null hypothesis is true? Older Adults (X); 52,52,60,48,51,57,43,55,50,51 Younger Adults (Y); 42,40,38,40,36,47,43,38,39,40
Explanation / Answer
a
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given that,
mean(x)=51.9
standard deviation , s.d1=4.72
number(n1)=10
y(mean)=40.3
standard deviation, s.d2 =3.09
number(n2)=10
null, Ho: u1 = u2
alternate,older adults have a higher life satisfaction score than younger adults H1: u1 > u2
level of significance, = 0.05
from standard normal table,right tailed t /2 =1.734
since our test is right-tailed
reject Ho, if to > 1.734
calculate pooled variance s^2= (n1-1*s1^2 + n2-1*s2^2 )/(n1+n2-2)
s^2 = (9*22.2784 + 9*9.5481) / (20- 2 )
s^2 = 15.91325
we use test statistic (t) = (x-y)/sqrt(s^2(1/n1+1/n2))
to=51.9-40.3/sqrt((15.91325( 1 /10+ 1/10 ))
to=11.6/1.783998
to=6.502248
| to | =6.502248
critical value
the value of |t | with (n1+n2-2) i.e 18 d.f is 1.734
we got |to| = 6.502248 & | t | = 1.734
make decision
hence value of | to | > | t | and here we reject Ho
p-value: right tail -ha : ( p > 6.5022 ) = 0
hence value of p0.05 > 0,here we reject Ho
ANSWERS
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b.
null, Ho: u1 = u2
alternate, H1: u1 > u2
c.
test statistic: 6.502248
d.decision: reject Ho
the result figured is older adults have a higher life satisfaction score than younger adults
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