C still using our same sample results what one number

Info icon This preview shows pages 166–169. Sign up to view the full content.

View Full Document Right Arrow Icon
(c) Still using our same sample results, what one number would you use to predict a healthy body temperature? If you then considered the uncertainty (margin-of-error) in this estimate for predicting one person’s body temperature, would you expected this marg in-of-error to be larger or smaller then for predicting the population mean body temperature? Explain. Estimate: Margin-of-error: Explain: To construct such a confidence interval (often called a “prediction interval” to indicate that it will predict an individual outcome rather than the population mean), we need to consider both the sample-to- sample variation in sample means as well as the individual-to-individual variation in body temperatures. (d) We will estimate this combined standard error of an individual value by s n / 1 1 ² . Using this formula, how will this compare to the standard error of the sample mean (larger or smaller)? Explain. (e) Calculate this value for the body temperature data.
Image of page 166

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Chance/Rossman, 2015 ISCAM III Investigation 2.6 166 If we are willing to assume that the population follows a normal distribution (note this is more restrictive than what we need to apply the Central Limit Theorem), then we can construct a 95% prediction interval for an individual outcome using the t- distribution. Definition: To predict an individual value, we can calculate a prediction interval (PI) . We construct the interval using the sample mean as our estimate, but we adjust the standard error to take into account the additional variability of an individual value from the population mean: x + t * n ± 1 n s s / 2 2 ² or x + t * n ± 1 u s n / 1 1 ² This procedure is valid as long as the sample observations are randomly selected from a normally distributed population. Note that prediction intervals are not robust to violations from the normality condition even with large sample sizes. (f) Notice the critical value will be the same as in the previous investigation. Recall or determine the critical value with n = 130 and 95% confidence. (g) Using your answer to (f), calculate a 95% prediction interval for an individual healthy adult body temperature. (h) How do the center and width of this interval compare to the 95% confidence interval for the population mean body temperature found in the previous investigation? (i) Provide a one-sentence interpretation on the interval calculated in (g). (j) The JAMA article only reported the summary statistics and did not provide the individual temperature values. If you had access to the individual data values, what could you do to assess whether the normality assumption is reasonable? (k) Without access to the individual data values but considering the context (body temperatures of healthy adults), do you have any thoughts about how plausible it is that the population is normally distributed?
Image of page 167
Chance/Rossman, 2015 ISCAM III Investigation 2.6 167 Study Conclusions For one person to determine whether they have an unusual body temperature, we need a prediction interval rather than a confidence interval for the population mean. A 95% prediction interval for the body temperature of a healthy adult turns out to be (96.79, 99.71), a fairly wide interval.
Image of page 168

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 169
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern