Answered: A study is conducted to investigate 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

A study is conducted to investigate the average number of hours of sleep per night for a sample of 40 college students. The sample mean is found to be x̄ = 6.5 hours with a standard deviation of s = 1.2 hours. Perform a hypothesis test to determine if the population mean number of hours of sleep per night is less than 7 hours. Use a significance level of α = 0.05.

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 + ...

Expert Solution

Step 1

Introduction :

Confidence intervals and hypothesis tests are two commonly used statistical techniques for making inferences about a population based on sample data. Confidence intervals provide a range of values that is likely to contain the population parameter with a specified level of confidence, while hypothesis tests are used to test the validity of a claim or assumption about a population parameter. In this answer, three different scenarios were presented where a confidence interval or hypothesis test was performed on data from a sample to make inferences about a population mean.