Answered: A simple random sample of size n is…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.5: Comparing Sets Of Data

Problem 13PPS

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Question

A simple random sample of size n is drawn from a population that is normally distributed. The sample mean,

is found to be

19.4,

and the sample standard deviation, s, is found to be

4.3.

(a) Construct a

95%

confidence interval about

if the sample size, n, is

31.

(b) Construct a

95%

confidence interval about

if the sample size, n, is

63.

How does increasing the sample size affect the margin of error, E?

(c) Construct a 98% confidence interval about μ if the sample size, n, is 31.
How does increasing the level of confidence affect the size of the margin of error, E?

(d) If the sample size is 21, what conditions must be satisfied to compute the confidence interval?

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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