A company wants to estimate the mean net weight of fertilizer cans for a particular kind of fertilizers. Assume that these weights are normally distributed. A random sample of the following 12 cans is collected : 15.6 15.9 16.2 16.0 15.6 16.2 15.9 16.0 15.6 15.7 16.0 16.2 Find a 98% confidence interval for the mean net weight of all the fertilizer cans.

Answered: A company wants to estimate the mean…

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

A company wants to estimate the mean net weight of fertilizer cans for a particular kind of fertilizers. Assume that these weights are normally distributed. A random sample of the following 12 cans is collected :

15.6 15.9 16.2 16.0 15.6 16.2

15.9 16.0 15.6 15.7 16.0 16.2

Find a 98% confidence interval for the mean net weight of all the fertilizer cans.

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.

Expert Solution

Step 1

Confidence interval give a range of values for the unknown parameter of the population. The width of confidence interval increases with increase in confidence level.

The t distribution is a distribution similar to normal distribution but having heaver tails. The t distribution is used when the population standard deviation is unknown or sample size is less than 30.