A group of students estimated the length of one minute without reference to a watch or clock, and the times (seconds) are listed below. Use a0.01significance level to test the claim that these times are from a population with a mean equal to 60 seconds. Does it appear that students are reasonably good at estimating one minute? 7893457250356673785876821039876 Question content area bottomPart 1Assuming all conditions for conducting a hypothesis test are met, what are the null and alternative hypotheses? A.H0:μ=60secondsH1:μ>60seconds B.H0:μ=60secondsH1:μ≠60secondsYour answer is correct. C.H0:μ=60secondsH1:μ<60seconds D.H0:μ≠60secondsH1:μ=60secondsPart 2Determine the test statistic.

Given data is78,93,45,72,50,35,66,73,78,58,76,82,103,98,76sample size(n)=15significance level(α)=0.01x x2 78 6084 93 8649 45 2025 72 5184 50 2500 35 1225 66 4356 73 5329 78 6084 58 3364 76 5776 82 6724 103 10609 98 9604 76 5776 ∑x=1083 ∑x2=83289 Mean(x)=∑xnMean(x)=108315Mean(x)=72.2standard deviation(s)=∑x2-(∑x)2nn-1s=83289-(1083)21515-1s≅19.0795The null and alternative hypothesis isH0:μ=60 secondsH1:μ≠60 secondsThe correct option is "B"Test statistic(t):-t=x-μsnt=72.2-6019.079515t=2.4765The test statistic is 2.4765P-value:-Degrees of freedom(df)=n-1=15-1=142P(t>2.4765)=0.0266 (from excel formula)P-value is 0.0266P-value is greater than significance level(α)=0.01Hence Fail to reject H0There is no sufficient evidence to support the claim that these times are from a population with a mean is not equal to 60 seconds

Answered: A group of students estimated 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 content area bottom

Part 1

Assuming all conditions for conducting a hypothesis test are met, what are the null and alternative hypotheses?

H0:

μ=60

seconds

H1:

μ>60

seconds

H0:

μ=60

seconds

H1:

μ≠60

seconds

Your answer is correct.

H0:

μ=60

seconds

H1:

μ<60

seconds

H0:

μ≠60

seconds

H1:

μ=60

seconds

Part 2

Determine the test statistic.

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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