Determine the 90% confidence interval for a sample, taken from a normally distributed population, that has a mean of 685, a sample standard deviation of 74, and a sample size of 29
To determine the 90% confidence interval for a sample, we can use the formula:
Confidence interval = sample mean ± (critical value) * (sample standard deviation / sqrt(sample size))
To find the critical value, we can refer to the standard normal distribution table or use a statistical calculator. For a 90% confidence level, the critical value is approximately 1.645.
Plugging in the given values:
Confidence interval = 685 ± (1.645) * (74 / sqrt(29))
Calculating the square root of the sample size:
Confidence interval = 685 ± (1.645) * (74 / 5.39)
Dividing the sample standard deviation by the square root of the sample size:
Confidence interval = 685 ± (1.645) * (13.72)
Calculating the product of the critical value and the result:
Confidence interval = 685 ± 22.58
Therefore, the 90% confidence interval for the population mean is (662.42, 707.58).
To determine the 90% confidence interval for a sample, taken from a normally distributed population, we can use the formula:
Confidence Interval = sample mean ± (critical value * standard error)
1. Calculate the standard error:
Standard Error = sample standard deviation / √(sample size)
Therefore, in this case:
Standard Error = 74 / √(29)
2. Determine the critical value:
For a 90% confidence level, we need to find the critical value associated with a 5% significance level (since 100% - 90% = 10% = 5% on each tail).
The critical value can be obtained from a t-distribution table or using statistical software. For a sample size of 29, the critical value is approximately 1.699.
3. Calculate the confidence interval:
Confidence Interval = 685 ± (1.699 * (74 / √(29)))
Lower bound = 685 - (1.699 * (74 / √(29)))
Upper bound = 685 + (1.699 * (74 / √(29)))
Evaluate the lower and upper bounds to get the 90% confidence interval.
By following these steps, you can calculate the 90% confidence interval for the given sample.