Answered: investigate whether a new training…

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

An owner of an ice cream shop wants to investigate whether a new training program affects the scooping skills of ice cream shop employees. To assess this, the owner divides employees into two groups: those who receive training (CT) and those who do not (NT). The owner evaluates their scooping skills using a scooping proficiency test. The dataset includes the test scores of the NT (no training) group: 15.00, 7.00, 18.00, 10.00, 6.00, and 20.00, and the CT (trained) group: 15.00, 10.00, 14.00, 7.00, 21.00, and 21.00. The owner is aware of the known population mean for scooping proficiency, which is 20. The hypothesis is that employees who did not receive training (NT) will likely have lower scooping proficiency than the population mean. To investigate this hypothesis, the owner conducts a one-sample t-test with a significance level (alpha) set at 0.05. The objective is to determine if the mean scooping proficiency of the NT group is significantly different from the established population mean of 20, using a one-sample t-test.

what is the sample standard deviation?

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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