Bio space Life Sciences study survey of small Population was conducted to examin
ID: 2933379 • Letter: B
Question
Bio space Life Sciences study survey of small Population was conducted to examine the differences between older and younger adults on their contentment with their life. A pilot experiment was conducted in New York to examine this hypothesis. Nine older adults (over the age of 75) and nine younger adults (between 25 and 35) were give a life satisfaction test (known to have a high reliability and validity). Scores on the measure range from 0 to 100 with high scores indicative of high life satisfaction; low scores indicative of low life satisfaction at confidence levels of 90%. The date are presented below. Computer the appropriate t-tst. What is the compted answer (observed value of t) and df? What would be the null and hypothesis in this study? What is your tcrit? Conclude your answer? If you have man error, would it be a Type 1 or Type 2 error? Explain your answer.
older adults 90,66, 63, 88, 50, 90, 85, 76, 36
younger adults 50 44, 45, 65, 52, 52, 38, 55, 44
Explanation / Answer
Given that,
null, H0: Ud = 0
alternate, H1: Ud > 0
level of significance, = 0.1
from standard normal table,right tailed t /2 =1.397
since our test is right-tailed
reject Ho, if to > 1.397
we use Test Statistic
to= d/ (S/n)
where
value of S^2 = [ di^2 – ( di )^2 / n ] / ( n-1 ) )
d = ( Xi-Yi)/n) = 22.11
We have d = 22.11
pooled variance = calculate value of Sd= S^2 = sqrt [ 7099-(199^2/9 ] / 8 = 18.37
to = d/ (S/n) = 3.61
critical Value
the value of |t | with n-1 = 8 d.f is 1.397
we got |t o| = 3.61 & |t | =1.397
make Decision
hence Value of | to | > | t | and here we reject Ho
p-value :right tail - Ha : ( p > 3.6113 ) = 0.00343
hence value of p0.1 > 0.00343,here we reject Ho
ANSWERS
---------------
null, H0: Ud = 0
alternate, H1: Ud > 0
test statistic: 3.61
critical value: reject Ho, if to > 1.397
decision: Reject Ho
p-value: 0.00343
we have enough evidence to support the claim
decision is reject Ho,
so that error is Type1 error, where Ho is true
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