In one city, the average amount of time that tenth-graders spend watching television each week is 23 hours. The principal of Birchwood High School believes it is less for the 10th grade students that at his school. For a sample of 95 tenth-graders from the school, the mean amount of time spent watching television per week was 21.9 hours. Assuming a population standard deviation of 3.1 hours, does the data provide sufficient evidence to conclude that for all tenth-graders at Birchwood High school, the mean amount of time spent watching television per week is less than the city average of 23 hours? Perform the appropriate hypothesis test using a significance level of 0.005. What are the hypotheses? What is the test statistic? Is it a z or a t? Find the P-value for this test statistic. How does it compare to the significance level? On the normal curve, indicate the location of the test statistic and the p-value. (label them on the graph) Write a conclusion in statistical terms and relate it to the parameters of this problem.

GivenMean(x)=21.9population standar deviation(σ)=3.1sample size(n)=95α=0.005

Answered: In one city, the average amount of time…

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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In one city, the average amount of time that tenth-graders spend watching television each week is 23 hours. The principal of Birchwood High School believes it is less for the 10^th grade students that at his school. For a sample of 95 tenth-graders from the school, the mean amount of time spent watching television per week was 21.9 hours. Assuming a population standard deviation of 3.1 hours, does the data provide sufficient evidence to conclude that for all tenth-graders at Birchwood High school, the mean amount of time spent watching television per week is less than the city average of 23 hours? Perform the appropriate hypothesis test using a significance level of 0.005.
What are the hypotheses?

What is the test statistic? Is it a z or a t?

Find the P-value for this test statistic. How does it compare to the significance level? On the normal curve, indicate the location of the test statistic and the p-value. (label them on the graph)

Write a conclusion in statistical terms and relate it to the parameters of this problem.

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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