The null and alternate hypotheses are: H0 : 1 = 2 H1 : 1 2 A random sample of 10
ID: 3340869 • Letter: T
Question
The null and alternate hypotheses are: H0 : 1 = 2 H1 : 1 2
A random sample of 10 observations from one population revealed a sample mean of 23 and a sample standard deviation of 4. A random sample of 8 observations from another population revealed a sample mean of 26 and a sample standard deviation of 5. At the 0.05 significance level, is there a difference between the population means?
3. State the decision rule. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.)
4.Compute the pooled estimate of the population variance. (Round your answer to 3 decimal places.)
A nationwide sample of influential Republicans and Democrats was asked as a part of a comprehensive survey whether they favored lowering environmental standards so that high-sulfur coal could be burned in coal-fired power plants. The results were: Republicans Democrats Number sampled 1,000 800 Number in favor 200 168 Hint: For the calculations, assume the Democrats as the first sample.
5. Determine the p-value. (Round your answer to 4 decimal places.)
Explanation / Answer
Q1.
Given that,
mean(x)=23
standard deviation , s.d1=4
number(n1)=10
y(mean)=26
standard deviation, s.d2 =5
number(n2)=8
null, Ho: u1 = u2
alternate, H1: u1 != u2
level of significance, = 0.05
from standard normal table, two tailed t /2 =2.12
since our test is two-tailed
reject Ho, if to < -2.12 OR if to > 2.12
calculate pooled variance s^2= (n1-1*s1^2 + n2-1*s2^2 )/(n1+n2-2)
s^2 = (9*16 + 7*25) / (18- 2 )
s^2 = 19.9375
we use test statistic (t) = (x-y)/sqrt(s^2(1/n1+1/n2))
to=23-26/sqrt((19.9375( 1 /10+ 1/8 ))
to=-3/2.118003
to=-1.416428
| to | =1.416428
critical value
the value of |t | with (n1+n2-2) i.e 16 d.f is 2.12
we got |to| = 1.416428 & | t | = 2.12
make decision
hence value of |to | < | t | and here we do not reject Ho
p-value: two tailed ( double the one tail ) - ha : ( p != -1.4164 ) = 0.1747
hence value of p0.05 < 0.1747,here we do not reject Ho
we don't have evidence to claim difference between the population mean
ANSWERS
---------------
a.
decision rule : reject Ho, if to < -2.12 OR if to > 2.12
b.
calculate pooled variance s^2= (n1-1*s1^2 + n2-1*s2^2 )/(n1+n2-2)
s^2 = (9*16 + 7*25) / (18- 2 )
s^2 = 19.9375
Q2.
Given that,
sample one, x1 =200, n1 =1000, p1= x1/n1=0.2
sample two, x2 =168, n2 =800, p2= x2/n2=0.21
null, Ho: p1 > p2
alternate, H1: p1 < p2
level of significance, = 0.025
from standard normal table,left tailed z /2 =1.96
since our test is left-tailed
reject Ho, if zo < -1.96
we use test statistic (z) = (p1-p2)/(p^q^(1/n1+1/n2))
zo =(0.2-0.21)/sqrt((0.204*0.796(1/1000+1/800))
zo =-0.523
p-value: left tail - Ha : ( p < -0.5227 ) = 0.30058