The average annual cost of the first year of owning and caring for a large dog is $1,843 (US News and World Report, September 9, 2013). 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 = $255.
a. Using this sample, what is the 95% confidence interval for the mean cost of the first year of owning and caring for an Irish Red and White Setter (to 2 decimals)?
To calculate the 95% confidence interval for the mean cost of the first year of owning and caring for an Irish Red and White Setter, we can use the formula:
Confidence Interval = Sample Mean +/- Margin of Error
The margin of error depends on the sample size, sample mean, and population standard deviation. The formula for the margin of error is:
Margin of Error = (Z-value) * (σ / √n)
Where:
- Z-value represents the critical value from the standard normal distribution that corresponds to the desired confidence level. For a 95% confidence level, the Z-value is approximately 1.96.
- σ (sigma) is the population standard deviation.
- n is the sample size.
Given the information provided:
Sample size (n) = 50
Population standard deviation (σ) = $255
To calculate the sample mean, we need additional information. Unfortunately, the mean cost for the first year of owning and caring for an Irish Red and White Setter is not provided in the question. Once that value is available, we can proceed with the calculation.
Please provide the sample mean for the first year cost, and we can continue with calculating the 95% confidence interval.