For a sample size of 10 from a population whose standard deviation is not known, which type of probability distribution is used to help calculate a confidence interval for the mean?
To calculate a confidence interval for the mean when the standard deviation is not known, you would typically use the t-distribution. The t-distribution is a probability distribution that is used when the sample size is small or when the population standard deviation is unknown.
To calculate a confidence interval using the t-distribution, you need three pieces of information: the sample mean, the sample standard deviation, and the sample size. The formula for the confidence interval is:
Confidence Interval = sample mean ± (t-value * standard error)
Here, the t-value is determined based on the desired confidence level and the degrees of freedom, which is calculated as (sample size - 1). The standard error is the estimated standard deviation of the sample mean and is calculated as the sample standard deviation divided by the square root of the sample size.
To find the t-value, you can refer to a t-distribution table or use statistical software. The t-value is dependent on the desired confidence level and the degrees of freedom. The higher the confidence level, the larger the t-value and wider the confidence interval.
So, in your case, since you have a sample size of 10 and the population standard deviation is not known, you would use the t-distribution to calculate the confidence interval for the mean. Remember to determine the appropriate degrees of freedom and the corresponding t-value based on the desired confidence level.