11. A local health care company wants to estimate the mean weekly elder day care cost. A sample of 10 facilities shows a mean of $250 per week with a standard deviation of $25. What is the 90 percent confidence interval for the population mean?
Use a confidence interval formula:
CI90 = mean ± 1.645(sd/√n)
...where ± 1.645 represents the 90% confidence interval using a z-table, sd = standard deviation, √ = square root, and n = sample size.
Plug your data into the formula to calculate the confidence interval.
I hope this will help get you started.
To calculate the 90 percent confidence interval for the population mean, you can use the formula:
Confidence Interval = X̄ ± (Z * (σ / √n))
Where:
X̄ is the sample mean
Z is the z-score corresponding to the desired confidence level (in this case 90%, which corresponds to a z-score of 1.645)
σ is the population standard deviation
n is the sample size
In this case, the provided information is as follows:
Sample mean (X̄) = $250
Standard deviation (σ) = $25
Sample size (n) = 10
Step 1: Calculate the standard error of the mean.
Standard error = σ / √n
Standard error = $25 / √10
Step 2: Calculate the margin of error.
Margin of error = Z * standard error
Margin of error = 1.645 * ($25 / √10)
Step 3: Calculate the confidence interval.
Confidence Interval = X̄ ± margin of error
Confidence Interval = $250 ± (1.645 * ($25 / √10))
Now, calculate the confidence interval:
Confidence Interval = $250 ± (1.645 * ($25 / √10))
Substitute the values and calculate:
Confidence Interval = $250 ± (1.645 * $25 / √10)
Confidence Interval = $250 ± (1.645 * $7.905)
Confidence Interval = $250 ± $13.008
Confidence Interval = [$237.992, $262.008]
Therefore, the 90 percent confidence interval for the population mean is [$237.992, $262.008].