You may need to use the appropriate appendix table or technology to answer this question. Money reports that the average annual cost of the first year

Yasmin 2021-02-06 Answered
You may need to use the appropriate appendix table or technology to answer this question.
Money reports that the average annual cost of the first year of owning and caring for a large dog in 2017 is $1,448. 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 population standard deviation is assumed known with σ=$230.
1,9022,0421,9361,8171,5041,5721,5321,9071,8822,1531,9451,3352,0061,5161,8391,7391,4561,9581,9342,0941,7391,4341,6671,6791,7361,6701,7702,0521,3791,9391,8541,9132,1631,7371,8881,7372,2302,1311,8132,1181,9782,1661,4821,7001,6792,0601,6831,8502,2322,294
(a)
What is the margin of error for a 95% confidence interval of the mean cost in dollars of the first year of owning and caring for this breed? (Round your answer to nearest cent.)
(b)
The DATAfile 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 sample, what is the 95% confidence interval for the mean cost in dollars of the first year of owning and caring for an Irish Red and White Setter? (Round your answers to nearest cent.)
$_______ to $________
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Expert Answer

pattererX
Answered 2021-02-07 Author has 95 answers
Step 1
(a)
The known values are,
σ=230,
n=50
Critical value:
By using the z-tables, the critical value at 5% level of significance for a two tailed z-distribution is,
Z0.05/2=±1.96
The value of margin of error is
m=zα/2(σn)
=1.96(23050)
=1.96×32.52691
=63.75275
63.75
Thus, the required margin of error is m=63.75
Step 2
(b)
The sample mean is,
x=i1nxin
=1902+2042+1936+1817++2232+229450
=9184250
=1837
The 95% confidence interval for the mean cost in dollars of the first year of owning and caring for an Irish Red and White Setter is,
CI=x±m
=1837±63.75
=(183763.75,1837+63.75)
=(1773.25,1900.75)
Thus, the required confidence interval is, ($1773.25 to $1900.75)
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