Question

1. The average annual cost of the first year of owning and caring for a large dog is $1200. 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 o = $ 200. a. What is the 90% confidence interval of the mean cost of the first year of owning and caring for this breed? b. Explain the confidence interval obtained in a.

Answer 1

1)

a)

90% confidence interval for $\mu$ is

$\bar{x}$ - Z$\alpha$/2 * $\sigma$ / sqrt(n) < $\mu$ < $\bar{x}$ + Z$\alpha$/2 * $\sigma$ / sqrt(n)

1200 - 1.645 * 200 / sqrt(50) < $\mu$ < 1200 + 1.645 * 200 / sqrt(50)

1153.47 < $\mu$ < 1246.53

90% CI is ( 1153.47 , 1246.53 )

b)

We are 90% confident that the mean cost of first year of owning and caring for this breed is between

$1153.47 and $1246.53