Answered: (a) Calculate the sampling error at 95%…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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A research team is working on a project to study the time (in seconds) for high school male runners to finish a 400-meter race. Jimmy, a junior researcher in the team, has randomly selected a sample of 25 male runners from a high school and the time (in seconds) for each of them to complete a 400-meter race was recorded. The sample mean running time was 53 seconds. It is assumed that the running time in a 400-meter race follows a normal distribution with a population standard deviation of 5.5 seconds.

(a) Calculate the sampling error at 95% confidence level

(b) Construct a 95% confidence interval estimate of the population mean running time for a 400-meter race.

(c) If instead of 25, 80 male runners are selected for the study, what is the sampling error at 95% confidence level? When the 95% confidence interval is constructed based on a sample with 80 male runners, wouldyou expect the interval will be (I) narrower, (II) wider, or (III the same width as the confidence interval constructed in part (b)?

(d) After discussion with the research director, Jimmy is asked to work on the research again. This time, he needs to ensure the difference between the point estimate and the true population mean be within +- 0.8 seconds at 99% confidence level. To fulfil the requirement, how large should be the minimum sample size?

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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