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.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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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.