This is just a homework I am trying to understand. I noticed x bar was not given but the population mean is given. Is this something like paired t test? Kindly help solve. Thank you! EXERCISE 10-9Exercises for Chapter 10In a tomato processing factory, the drained weight after filling cans of tomatoesin puree averages 21.8 ounces during the morning. One afternoon, a qualitycontrol worker selects five cans of tomatoes filled that afternoon and weighs345the drained contents in ounces (based on Duncan, 1974, page 569; Grant andLeavenworth, 1972, page 41):19.0 19.5 19.5 20.5 21.5a. Plot the observations.b. Use at distribution to test the null hypothesis that the average drainedweight in cans filled that afternoon equaled 21.8 ounces. Calculate a confi-dence interval for the average afternoon drained weight.c. Repeat part (b) using a Wilcoxon signed rank distribution.d. Use a binomial distribution to test the null hypothesis that the mediandrained weight in cans filled that afternoon equaled 21.8 ounces. Calculatea confidence interval for the median afternoon drained weight.e. Compare your results in parts (b), (c), and (d). Discuss your findings.

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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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This is just a homework I am trying to understand. I noticed x bar was not given but the population mean is given. Is this something like paired t test? Kindly help solve. Thank you!

EXERCISE 10-9
Exercises for Chapter 10
In a tomato processing factory, the drained weight after filling cans of tomatoes
in puree averages 21.8 ounces during the morning. One afternoon, a quality
control worker selects five cans of tomatoes filled that afternoon and weighs
345
the drained contents in ounces (based on Duncan, 1974, page 569; Grant and
Leavenworth, 1972, page 41):
19.0 19.5 19.5 20.5 21.5
a. Plot the observations.
b. Use at distribution to test the null hypothesis that the average drained
weight in cans filled that afternoon equaled 21.8 ounces. Calculate a confi-
dence interval for the average afternoon drained weight.
c. Repeat part (b) using a Wilcoxon signed rank distribution.
d. Use a binomial distribution to test the null hypothesis that the median
drained weight in cans filled that afternoon equaled 21.8 ounces. Calculate
a confidence interval for the median afternoon drained weight.
e. Compare your results in parts (b), (c), and (d). Discuss your findings.

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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