Final answer:
The t distribution is used to develop a confidence interval estimate of the population proportion when the population standard deviation is unknown. We use the sample standard deviation as an estimate in this case. To construct a confidence interval estimate, we calculate the sample mean and standard deviation, find the appropriate t-score, calculate the margin of error, and interpret the confidence interval.
Step-by-step explanation:
The t distribution is used to develop a confidence interval estimate of the population proportion when the population standard deviation is unknown. When we don't have information about the population standard deviation, we use the sample standard deviation as an estimate. The t-distribution is more accurate than the normal distribution in this case.
To construct a confidence interval estimate for an unknown population mean using the t distribution, we need data from a random sample. The steps to construct and interpret the confidence interval are:
- Calculate the sample mean and standard deviation.
- Find the appropriate t-score from the t-table based on the desired confidence level and degrees of freedom.
- Calculate the margin of error by multiplying the t-score with the standard deviation divided by the square root of the sample size.
- Calculate the lower and upper bounds of the confidence interval by subtracting and adding the margin of error to the sample mean, respectively.
- Interpret the confidence interval, which represents the range of values within which we are confident the population mean lies.