Question

Researchers from a certain country were interested in how characteristics of the spleen of residents in their tropical environment compare to those found elsewhere in the world. The researchers randomly sampled 93 males and 107 females in their country. The mean and standard deviation of the spleen lengths for the males were 112 cm and 0.9 cm, respectively, and those for the females were 10.3 cm and 0.7 cm, respectively. At the 5% significance level do the data provide sufficient evidence to conclude that a difference exists in the mean spleen lengths of males and females in the country? Assume the population standard deviations are equal Click here to view page 1 of the table of critical values of t. Click here to view page 2 of the table of critical values of t. Let population 1 be all males in the country and let population 2 be all females in the country. What are the correct hypotheses to test? O A. Ho H, H2 HH <H₂ Oc. Ho H = H₂ H₂ H H₂ B. H. Hy #Hz Ha Hy = H₂ OD. HOH, CH2 H .H2 Click to select your answer(s). x 7/8/20 O Type here to search E II

Answer 1

Given that,
mean(x)=11.2
standard deviation , s.d1=0.9
number(n1)=93
y(mean)=10.3
standard deviation, s.d2 =0.7
number(n2)=107
null, Ho: u1 = u2
alternate, H1: u1 != u2
level of significance, α = 0.05
from standard normal table, two tailed t α/2 =1.972
since our test is two-tailed
reject Ho, if to < -1.972 OR if to > 1.972
calculate pooled variance s^2= (n1-1*s1^2 + n2-1*s2^2 )/(n1+n2-2)
s^2 = (92*0.81 + 106*0.49) / (200- 2 )
s^2 = 0.639
we use test statistic (t) = (x-y)/sqrt(s^2(1/n1+1/n2))
to=11.2-10.3/sqrt((0.639( 1 /93+ 1/107 ))
to=0.9/0.113
to=7.942
| to | =7.942
critical value
the value of |t α| with (n1+n2-2) i.e 198 d.f is 1.972
we got |to| = 7.942 & | t α | = 1.972
make decision
hence value of | to | > | t α| and here we reject Ho
p-value: two tailed ( double the one tail ) - ha : ( p != 7.9416 ) = 0
hence value of p0.05 > 0,here we reject Ho
ANSWERS
---------------
null, Ho: u1 = u2
alternate, H1: u1 != u2
test statistic: 7.942
critical value: -1.972 , 1.972
decision: reject Ho
p-value: 0
we have enough evidence to support the claim that difference of means of length between males and females in the country.