A manufacturer of widgets wants to test a new widget-producing machine to determine if it can make an average of 25 widgets per second before deciding to invest in the machine. The standard to reject the new machine is if it makes an average of less than 25 widgets per second. Here are data from a small random sample:25.6, 26.2, 22.5, 20.5, 26.4, 27.4, 23.6, 26.9, 25.7, 24.9Assuming the population follows a normal distribution, is there evidence that the new machine should be rejected at the 0.01 significance level? State the hypotheses, list and check the conditions, calculate the test statistic, find the p-value, and make a conclusion in a complete sentence related to the scenario.

We have given that Sample size n =10 First I want to find mean and standard deviation Mean = sum…

Answered: A manufacturer of widgets wants to test…

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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A manufacturer of widgets wants to test a new widget-producing machine to determine if it can make an average of 25 widgets per second before deciding to invest in the machine. The standard to reject the new machine is if it makes an average of less than 25 widgets per second. Here are data from a small random sample:

25.6, 26.2, 22.5, 20.5, 26.4, 27.4, 23.6, 26.9, 25.7, 24.9

Assuming the population follows a normal distribution, is there evidence that the new machine should be rejected at the 0.01 significance level? State the hypotheses, list and check the conditions, calculate the test statistic, find the p-value, and make a conclusion in a complete sentence related to the scenario.

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.

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