Answered: .6.1 Experience has shown that 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

Q.6.1
Experience has shown that the diameter of a machined component is normally distributed, with an average diameter (μ) of 165mm, and a standard deviation (σ) of 2.5mm. A sample of 77 components is randomly selected.

Q.6.1.1
Determine the standard error for this sample.

Q.6.1.2
What is the probability that the mean diameter of the components in the sample will lie between 164.25mm and 164.75mm? Interpret your answer.

Q.6.2
It has been found that 14% of customers of an online retail store wait longer than five days for their order to be delivered. We assume normal distribution, and randomly select 115 customers.

Q.6.2.1
Determine the standard error for this sample.

Q.6.2.2
What is the probability that, for the sample of 115 customers, the proportion who wait longer than five days for their order to be delivered is less than 13.75%? Interpret your answer.

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Question 7
Q.7.1
Explain the difference between a Type I error and a Type II error.

Q.7.2
Explain the connection between the significance level and a Type I error.

Question 8
Q.8.1
A large manufacturing company claims that more than 88% of its customers are fully satisfied with the company’s products. Test this claim at the 5% significance level, if a survey found that 360 out of a random sample of 400 of the company’s customers said that they were fully satisfied with the company’s products.

Q.8.2
The CEO of Global Investment Funds claims that, on average, clients leave their investment funds with the company for a period of at least 56 months.
Test this claim at the 10% significance level, if it was found that a sample of 29 clients left their investment funds with the company for an average period of 58.85 months, with a standard deviation of 3.75 months.

Q.8.3
A shop owner claims that on average, his shop has a daily turnover of R75 000. Test this claim at the 5% significance level, if the average daily turnover for a sample of 88 days was R71 500. Assume a population standard deviation of R4 450.

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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