Answered: The marketing director concluded, with…

The marketing director concluded, with 95% confidence, that between $113.36 and $130.64 contains the mean cost of all running shoes.

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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Question

A marketing director wants a 95% confidence interval for the mean cost of running shoes. She randomly samples 40 pairs of shoes and finds that the sample mean, ¯xx¯, was $122 with a sample standard deviation, ss, of $27.

The marketing director concluded, with 95% confidence, that between $113.36 and $130.64 contains the mean cost of all running shoes.

What would change for a narrower confidence interval?

Select all answers that will make the width narrower.

If the point estimate was larger.
If the sample size increased to 50 pairs of shoes.
If she increased the confidence level to a 99% confidence level.
If the sample standard deviation was larger.
If the point estimate was smaller.
If the sample standard deviation was smaller.
If the sample size decreased to 30 pairs of shoes.
If she decreased the confidence level to a 90% confidence interval.

Definition Definition Number of subjects or observations included in a study. A large sample size typically provides more reliable results and better representation of the population. As sample size and width of confidence interval are inversely related, if the sample size is increased, the width of the confidence interval decreases.

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