We are 95 confident meaning if we were to repeat this

Info icon This preview shows pages 165–167. Sign up to view the full content.

View Full Document Right Arrow Icon
We are 95% confident, meaning if we were to repeat this procedure on thousands of random samples, in the long-run roughly 95% of the resulting intervals would successfully capture the population mean. We believe these procedures are valid because the sample size of 130 should be large enough unless there is severe skewness or outliers in the population. Practice Problem 2.5A Explore the last statements in the above results box using t confidence intervals: (a) Continue with the Simulating Confidence Intervals applet. Explore the coverage rate of the t - procedure with random samples from an Exponential (skewed) population for n = 5, n = 100, and n = 200. Assess and summarize the performance of this t -procedure in each case. (b) Repeat (a) for a Uniform population distribution with endpoints a = 80 and b = 85. Practice Problem 2.5B A study conducted by Stanford researchers asked children in two elementary schools in San Jose, CA to keep track of how much television they watch per week. The sample consisted of 198 children. The mean time spent watching television per week in the sample was 15.41 hours with a standard deviation of 14.16 hours. (a) Carry out a one-sample t -test to determine whether there is convincing evidence that average amount of television watching per week among San Jose elementary children exceeds fourteen hours per week. (Report the hypotheses, test statistic, p-value, and conclusion at the 0.10 level of significance.) (b) Calculate and interpret a one-sample 90% t -confidence interval for the population mean. (c) Comment on whether the technical conditions for the t -procedures are satisfied here. [ Hint : What can you say based on the summary statistics provided about the likely shape of the population?]
Image of page 165

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

View Full Document Right Arrow Icon
Chance/Rossman, 2015 ISCAM III Investigation 2.6 165 Investigation 2.6: Healthy Body Temperatures (cont.) Reconsider the research question of Investigation 2.5 where a “one -sample t - test” found convincing evidence with sample mean body temperature of x = 98.249 0 F and a sample standard deviation of s = 0.733 0 F against the hypothesis that P = 98.6 in the population. In fact, we were 95% confident that P actually fell between 98.122 and 98.376 degrees (so not all that far from 98.6). (a) So if you recorded a body temperature of 98.6 0 would you be convinced you were sick? What temperature values would you be concerned about? (b) Is it true that approximately 95% of the temperatures in the sample fall inside your confidence interval? What percentage does? Do you think 95% of the temperatures in the population fall within the confidence interval? Prediction Intervals It is very important to keep in mind that the confidence interval reported above only makes statements about the population mean, not individual body temperatures. But what if we instead wanted an interval to estimate the body temperature of a single randomly selected healthy adult rather than the population mean body temperature?
Image of page 166
Image of page 167
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