Question

1) A random sample of 20 male German Shepherds found that their average weight was 112 pounds with a standard deviation of 28 pounds. A random sample of 14 male Dobermans found that their average weight is 107 pounds with a standard deviation of 24 pounds. Assume that weights are normally distributed. Use the Statcato printout below and a 5% significance level to test the claim that the population mean average weight of male German Shepherds (population 1) is more than the population mean average weight of male Doberman Pinchers (population 2). What does this data indicate about the relationship between the weight and the type of dog? Please explain why or why not the categorical variable is related to the quantitive variable?

c) Check all of the assumptions for a two-population mean T-test. Explain your answers. Does the problem meets all the assumptions?

d) Write a sentence to explain the T-test statistic.

e) Use the test statistics and the critical value to determine if the sample data significantly disagrees with the null hypothesis. Explain your answer.

g) Use the P-value and significance level to determine if the sample data could have occurred

by random chance (sampling variability) or is it unlikely to random chance? Explain your answer.

Answer 1

1.

Given that,
mean(x)=112
standard deviation , s.d1=28
number(n1)=20
y(mean)=107
standard deviation, s.d2 =24
number(n2)=14
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 =112-107/sqrt((784/20)+(576/14))
to =0.5578
| to | =0.5578
critical value
the value of |t α| with min (n1-1, n2-1) i.e 13 d.f is 1.771
we got |to| = 0.55782 & | t α | = 1.771
make decision
hence value of |to | < | t α | and here we do not reject Ho
p-value:right tail - Ha : ( p > 0.5578 ) = 0.29322
hence value of p0.05 < 0.29322,here we do not reject Ho
ANSWERS
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c.
the assumptions for a two-population mean T-test
d.
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
null, Ho: u1 = u2
alternate, H1: u1 > u2
e.
test statistic: 0.5578
critical value: 1.771
decision: do not reject Ho
g.
p-value: 0.29322
we do not have enough evidence to support the claim that the population mean average weight of male German Shepherds (population 1) is more than the population mean average weight of male Doberman Pinchers (population 2).