Here are the weights, in pounds, of a sample of 13 adult female Golden Retriever
ID: 3157505 • Letter: H
Question
Here are the weights, in pounds, of a sample of 13 adult female Golden Retriever dogs:
59.0, 54.1, 53.7, 51.6, 57.5, 58.7, 58.0, 53.8, 48.9, 53.9, 51.6, 55.9, and 57.4.
A What are the degrees of freedom, and what's the critical value of t needed to construct a 95% confidence interval for the population mean weight of adult Golden Retrievers?
B Can we use t procedures to do inference for the mean weight of the population of adult Golden Retrievers? Explain, and include a sketch of a data plot.
C Construct a 95% confidence interval for the mean weight of the population of adult Golden Retrievers. Show your work.
D Suppose someone was to do a test of the hypothesis H0: = 52. Interpret the
0
confidence interval you obtained in part c of this problem as it pertains to this hypothesis.
Explanation / Answer
[ANSWERS]
a. degrees of freedom = 12
c.
Confidence Interval
CI = x ± t a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
ta/2 = t-table value
CI = Confidence Interval
Mean(x)=54.9308
Standard deviation( sd )=3.1215
Sample Size(n)=13
Confidence Interval = [ 54.9308 ± t a/2 ( 3.1215/ Sqrt ( 13) ) ]
= [ 54.9308 - 2.179 * (0.866) , 54.9308 + 2.179 * (0.866) ]
= [ 53.044,56.817 ]
d.
Set Up Hypothesis
Null, H0: U=52
Alternate, H1: U!=52
Test Statistic
Population Mean(U)=52
Sample X(Mean)=54.9308
Standard Deviation(S.D)=3.1215
Number (n)=13
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =54.9308-52/(3.1215/Sqrt(13))
to =3.385
| to | =3.385
Critical Value
The Value of |t | with n-1 = 12 d.f is 2.179
We got |to| =3.385 & | t | =2.179
Make Decision
Hence Value of | to | > | t | and Here we Reject Ho
P-Value :Two Tailed ( double the one tail ) -Ha : ( P != 3.3853 ) = 0.0054
Hence Value of P0.05 > 0.0054,Here we Reject Ho
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