A simple random sample of size n is drawn. The sample mean, x, is found to be 18.2, and the sample standard deviation, s, is found to be 4.9. LOADING... Click the icon to view the table of areas under the t-distribution. (a) Construct a 95% confidence interval about μ if the sample size, n, is 34. Lower bound: 16.4916.49; Upper bound: 19.9119.91 (Use ascending order. Round to two decimal places as needed.) (b) Construct a 95% confidence interval about μ if the sample size, n, is 61. Lower bound: 16.9516.95; Upper bound: 19.4619.46 (Use ascending order. Round to two decimal places as needed.) How does increasing the sample size affect the margin of error, E? A. The margin of error does not change. B. The margin of error decreases. Your answer is correct. C. The margin of error increases. (c) Construct a 99% confidence interval about μ if the sample size, n, is 34. Lower bound: 15.9015.90; Upper bound: 20.5020.50 (Use ascending order. Round to two decimal places as needed.) Compare the results to those obtained in part (a). How does increasing the level of confidence affect the size of the margin of error, E? A. The margin of error decreases. B. The margin of error increases. Your answer is correct. C. The margin of error does not change. (d) If the sample size is 15, what conditions must be satisfied to compute the confidence interval? A. The sample data must come from a population that is normally distributed with no outliers. Your answer is correct. B. The sample size must be large and the sample should not have any outliers. C. The sample must come from a population that is normally distributed and the sample size must be large.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Related questions

Question

A simple random sample of size n is drawn. The sample mean,

is found to be

18.2,

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

4.9.

Click the icon to view the table of areas under the t-distribution.

(a) Construct a

95%

confidence interval about

if the sample size, n, is

34.

Lower bound:

16.4916.49;

Upper bound: 19.9119.91

(Use ascending order. Round to two decimal places as needed.)

(b) Construct a

95%

confidence interval about

if the sample size, n, is

61.

Lower bound:

16.9516.95;

Upper bound: 19.4619.46

(Use ascending order. Round to two decimal places as needed.)

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

The margin of error does not change.

The margin of error decreases.

Your answer is correct.

The margin of error increases.

99%

confidence interval about

if the sample size, n, is

34.

Lower bound:

15.9015.90;

Upper bound: 20.5020.50

(Use ascending order. Round to two decimal places as needed.)

Compare the results to those obtained in part (a). How does increasing the level of confidence affect the size of the margin of error, E?

The margin of error decreases.

The margin of error increases.

Your answer is correct.

The margin of error does not change.

(d) If the sample size is

15,

what conditions must be satisfied to compute the confidence interval?

The sample data must come from a population that is normally distributed with no outliers.

Your answer is correct.

The sample size must be large and the sample should not have any outliers.

The sample must come from a population that is normally distributed and the sample size must be large.

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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