Final answer:
To find upper and lower bounds using a calculator, you can calculate two standard deviations above the mean after determining the mean and standard deviation, or you can work with confidence intervals to find the error bound and sample mean. Advanced calculators or software can compute percentiles and Student's t-probabilities.
Step-by-step explanation:
To apply a statistics calculator and find upper and lower bounds, one can use two different approaches. For finding the value that is two standard deviations above the mean, you would first calculate the mean (μ) and standard deviation (σ) using your calculator or computer. Then, to find the value that is two standard deviations above the mean, just compute μ + 2σ.
To find the sample mean or error bound from a confidence interval, you can also use two approaches:
- Calculate the error bound by subtracting the sample mean from the upper value of the confidence interval, or divide the difference between the upper and lower values of the confidence interval by 2.
- To find the sample mean, subtract the error bound from the upper value of the confidence interval.
Percentiles and Student's t-probabilities can be calculated with statistical software or advanced calculators. For example, the TI-83 and similar models use tcdf to find probabilities for a given range and degrees of freedom.
When constructing a 95 percent confidence interval for the true mean or proportion, you would sketch a graph labeling the point estimate, and the lower and upper bounds of the confidence interval.