In 1908, W. S. Gosset published the article \"The Probable Error of Mean\" (Biom
ID: 3223295 • Letter: I
Question
In 1908, W. S. Gosset published the article "The Probable Error of Mean" (Biometrica, Vol. 6). In this pioneering paper, written under the pseudonym "Student, " Gosset introduced what later became known as Student's t distribution. He used the data in Table 2, which gives the additional sleep in hours obtained by a sample of 10 patients using medication laevohysocyamine hydrobromide. (a) At 5% significance level, do these data provide sufficient evidence to conclude that laevohysocyamine hydrobromide is effective; that is, determine if data support the claim that population mean of additional sleep hours is greater than zero. Here x bar = 2.33 and s = 2 hours. (b) Interpret your answer in part (a).Explanation / Answer
Given that,
population mean(u)=2.33
sample mean, x =2.33
standard deviation, s =2
number (n)=10
null, Ho: <2.33
alternate, H1: >2.33
level of significance, = 0.05
from standard normal table,right tailed t /2 =1.833
since our test is right-tailed
reject Ho, if to > 1.833
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =2.33-2.33/(2/sqrt(10))
to =0
| to | =0
critical value
the value of |t | with n-1 = 9 d.f is 1.833
we got |to| =0 & | t | =1.833
make decision
hence value of |to | < | t | and here we do not reject Ho
p-value :right tail - Ha : ( p > 0 ) = 0.5
hence value of p0.05 < 0.5,here we do not reject Ho
ANSWERS
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null, Ho: <2.33
alternate, H1: >2.33
test statistic: 0
critical value: 1.833
decision: do not reject Ho
p-value: 0.5
we don't have enough support the claim