Consider the following hypothesis test. H 0 : 1 - 2 = 0 H a : 1 - 2 0 The follow
ID: 3223183 • Letter: C
Question
Consider the following hypothesis test.
H0: 1 - 2 = 0
Ha: 1 - 2 0
The following results are from independent samples taken from two populations.
a. What is the value of the test statistic (to 2 decimals)?
b. What is the degrees of freedom for the t distribution?
c. What is the p-value?
The area in the upper tail is Selectless than .005between .005 and .01between .01 and .025between .025 and .05between .05 and .10between .10 and .20greater than .20Item 3 ; two-tailed p-value is between Selectless than .01between .01 and .02between .02 and .05between .05 and .1between .1 and .20between .20 and 40greater than .40Item 4 .
d. At = .05, what is your conclusion?
p-value is Selectgreater than or equal to 0.05, rejectgreater than 0.05, do not rejectless than or equal to 0.05, rejectless than 0.05, do not rejectequal to 0.05, rejectnot equal to 0.05, rejectItem 5 H0
Sample 1 Sample 2 n1 = 35 n2 = 40 x1 = 13.6 x2 = 10.1 s1 = 5.3 s2 = 8.5Explanation / Answer
Given that,
mean(x)=13.6
standard deviation , s.d1=5.3
number(n1)=35
y(mean)=10.1
standard deviation, s.d2 =8.5
number(n2)=40
null, Ho: u1 = u2
alternate, H1: u1 != u2
level of significance, = 0.05
from standard normal table, two tailed t /2 =2.032
since our test is two-tailed
reject Ho, if to < -2.032 OR if to > 2.032
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =13.6-10.1/sqrt((28.09/35)+(72.25/40))
to =2.167
| to | =2.167
critical value
the value of |t | with min (n1-1, n2-1) i.e 34 d.f is 2.032
we got |to| = 2.16693 & | t | = 2.032
make decision
hence value of | to | > | t | and here we reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != 2.1669 ) = 0.037
hence value of p0.05 > 0.037,here we reject Ho
ANSWERS
---------------
null, Ho: u1 = u2
alternate, H1: u1 != u2
test statistic: 2.167
critical value: -2.032 , 2.032
decision: reject Ho
p-value: 0.037
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