Answered: Data on the weights (lb) of the…

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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Question

Data on the weights (lb) of the contents of cans of diet soda versus the contents of cans of the regular version of the soda is summarized to the right. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal.

A. The test statistic, t, is

(Round to two decimal places as needed.)

B. The P-value iS.

(Round to three decimal places as needed.)

C. Construct a confidence interval appropriate for the hypothesis test

lb less than mu 1 minus mu 2less than lb

(Round to three decimal places as needed.)

The table presents data comparing two groups: "Diet" and "Regular." The parameters and their values are as follows:

- \( \mu \): Population mean
- \( \mu_1 \) (Diet)
- \( \mu_2 \) (Regular)

- \( n \): Sample size
- Both groups have a sample size of 35.

- \( \overline{x} \): Sample mean (average weight)
- Diet: 0.78514 lb
- Regular: 0.81614 lb

- \( s \): Standard deviation
- Diet: 0.00442 lb
- Regular: 0.00748 lb

This table is often used to summarize statistical data in research studies, providing insights into the differences in means and variability between two groups under investigation.

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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