Question 1201518: 7. Cost of Dog Ownership. Money reports that the average annual cost of the first year of owning and caring for a large dog in 2017 is $1448. The Irish Red and White Setter Association of America has requested a study to estimate the annual first-year cost for owners of this breed. A sample of 50 will be used. Based on past studies, the popula- tion standard deviation is assumed known with σ = $255.
a. What is the margin of error for a 95% confidence interval of the mean cost of
the first year of owning and caring for this breed?
b. The file Setters contains data collected from fifty owners of Irish Setters on the
cost of the first year of owning and caring for their dogs. Use this data set to
compute the sample mean. Using this sumple, what is the 95% confidence inter-
val for the
Answer by math_tutor2020(3816)   (Show Source):
You can put this solution on YOUR website!
Part (a)
n = 50 = sample size
sigma = 255 = population mean
At 95% confidence, the z critical value is roughly z = 1.960
Use a table like this
https://www.sjsu.edu/faculty/gerstman/StatPrimer/t-table.pdf
to get that value. Look at the bottom row labeled "Z" and above the 95% confidence level.
A stats calculator can also compute this value.
Compute the margin of error for the mean.
E = z*sigma/sqrt(n)
E = 1.960*255/sqrt(50)
E = 70.6823938474072
E = 70.682394
This value is approximate.
Round this value however your teacher instructs.
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Part (b)
You mentioned a file of the data values, but you didn't post the actual data.
So I'm unable to do this part.
To compute the sample mean, add up the values and then divide by the number of values. Spreadsheet software is recommended.
The spreadsheet function named AVERAGE will do both of these steps at once to get the sample mean right away.
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