Question

= 16 locations in region I gave the A study of fox rabies in a country gave the following information about different regions and the accurrence of rabies in each region. A random sample of n following information about the number of cases of fox rabies near that location. x, Region I Data 2 8 8 8 6 8 8 1 3 3 3 2 5 1 4 6 A second random sample of n2 = 15 locations in region II gave the following information about the number of cases of fox rabies near that location. Xx: Region II Data 2 2 5 2 6 8 5 4 4 4 2 2 5 6 9 (i) Use a calculator with sample mean and sample standard deviation keys to calculate X, and s, in region I, and X, and s, in region II. (Round your answers to two decimal places.) (ii) Does this information indicate that there is a difference (either way) in the mean number of cases of fox rabies between the two regions? Use a 5% level of significance. (Assume the distribution of rabies cases in both regions is mound-shaped and approximately normal.) (a) What is the level of significance? State the null and alternate hypotheses. HO: H, = Fly; H: H Ilz o Holly = tzi Hq : My > H₂ o Holly = H₂i Hq ilq <H2 OHO: Hy > Hai H1 H1 = 12 (b) What sampling distribution will you use? What assumptions are you making? The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations. The Student's t. We assume that both population distributions are approximately normal with known standard deviations. The standard normal. We assume that both population distributions are approximately normal with known standard deviations. The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations. What is the value of the sample test statistic? (Test the difference 4. - 4. Do not use rounded values. Round your final answer to three decimal places.)

Answer 1

1.

Given that,
mean(x)=4.75
standard deviation , s.d1=2.6957
number(n1)=16
y(mean)=4.4
standard deviation, s.d2 =2.2297
number(n2)=15
null, Ho: u1 = u2
alternate, H1: u1 != u2
level of significance, α = 0.05
from standard normal table, two tailed t α/2 =2.145
since our test is two-tailed
reject Ho, if to < -2.145 OR if to > 2.145
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =4.75-4.4/sqrt((7.2668/16)+(4.97156/15))
to =0.3949
| to | =0.3949
critical value
the value of |t α| with min (n1-1, n2-1) i.e 14 d.f is 2.145
we got |to| = 0.39488 & | t α | = 2.145
make decision
hence value of |to | < | t α | and here we do not reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != 0.3949 ) = 0.699
hence value of p0.05 < 0.699,here we do not reject Ho
ANSWERS
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i.
mean(x)=4.75
standard deviation , s.d1=2.6957
number(n1)=16
y(mean)=4.4
standard deviation, s.d2 =2.2297
number(n2)=15
ii.
level of significance=0.05
a.
null, Ho: u1 = u2
alternate, H1: u1 != u2
b.
normal distribution, t test with known standard deviations
c.
test statistic: 0.3949
critical value: -2.145 , 2.145
p-value: 0.699
p value is >0.5
option:c
diagram shown in the figure.
d.
decision: do not reject Ho
option:A
e.
option:D
we do not have enough evidence to support the claim that difference ofmean number of cases
for rabies between two regions.

2.
Given that,
mean(x)=12.5143
standard deviation , s.d1=2.4089
number(n1)=14
y(mean)=10.3978
standard deviation, s.d2 =2.3716
number(n2)=16
null, Ho: u1 = u2
alternate, H1: u1 > u2
level of significance, α = 0.05
from standard normal table,right tailed t α/2 =1.771
since our test is right-tailed
reject Ho, if to > 1.771
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =12.5143-10.3978/sqrt((5.8028/14)+(5.62449/16))
to =2.4182
| to | =2.4182
critical value
the value of |t α| with min (n1-1, n2-1) i.e 13 d.f is 1.771
we got |to| = 2.41824 & | t α | = 1.771
make decision
hence value of | to | > | t α| and here we reject Ho
p-value:right tail - Ha : ( p > 2.4182 ) = 0.0155
hence value of p0.05 > 0.0155,here we reject Ho
ANSWERS
---------------
i.
mean(x)=12.51
standard deviation , s.d1=2.41
number(n1)=14
y(mean)=10.39
standard deviation, s.d2 =2.37
number(n2)=16
ii.
level of significance =0.05
a.
option:C
null, Ho: u1 = u2
alternate, H1: u1 > u2
b.
standard t test with normal distribution with known standard deviations.
c.
test statistic: 2.4182
critical value: 1.771
c.
p-value: 0.0155
0.005 < p value <0.02
option:D
diagram shown
d.
option:C
decision: reject Ho
e.
option:D
we have enough evidence to support the claim that field A is higher than soil water contain in field B.