In a few more weeks, you will be adding a new member to your family – a 10-week
ID: 3073229 • Letter: I
Question
In a few more weeks, you will be adding a new member to your family – a 10-week old golden retriever puppy! In previous litters, the average weight of 42 puppies at 10 weeks was 14.8 lbs with a standard deviation of 1.1 lbs.
Find the 90% confidence interval for the average 10-week weight for golden retriever puppies. Show/explain your work, and identify the following:
a. The estimated population mean and degrees of freedom
b. The assumptions you are making for this calculation
c. The critical value for the distribution
d. The margin of error
e. The 90% CI, stated as a complete sentence
Explanation / Answer
a)
the mean is 14.8
df = n-1 = 42-1 = 41
sd=1.1
the critical value is calculated using the z table as the alpha = 0.1 , for 90% CI
1.2816
for 90% confidence interval the value is 1.645
the margin of error is
MOE = Z*SD/sqrt(n)
= 1.645*1.1/sqrt(42) = 0.279
The confidence interval is given as
mean +- MOE
14.8 +- 0.279
14.52 and 15.07
this means that we are 90% confident that the true value of the mean would lie in the range 14.52 and 15.07
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