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 = $250.

1,902	2,042	1,936	1,817	1,504	1,572	1,532	1,907	1,882	2,153
1,945	1,335	2,006	1,516	1,839	1,739	1,456	1,958	1,934	2,094
1,739	1,434	1,667	1,679	1,736	1,670	1,770	2,052	1,379	1,939
1,854	1,913	2,163	1,737	1,888	1,737	2,230	2,131	1,813	2,118
1,978	2,166	1,482	1,700	1,679	2,060	1,683	1,850	2,232	2,294

(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.)

Answer 1

a)

sample size    n=	50.00
std deviation σ=	250.000
std error ='σx=σ/√n=	35.3553

for 95 % CI value of z=		1.960
margin of error E=z*std error =		69.30

b)

sample mean 'x̄=

1837.00

lower bound=sample mean-E=		1767.70
Upper bound=sample mean+E=		1906.30
from above 95% confidence interval for population mean =(1767.70 ,1906.30)