A random sample of 100 students is taken from a larger population of students in a multi-lecture course and the sample mean (average) of their final grades is found to be 57.5. Suppose it is known that the population standard deviation is 5. Use R to help you test, with a significance level of 0.01, whether there is significant evidence that the average grade for the population exceeds 56. Choose the most correct statement.a.You test Ho: µ < 56 versus Ha: µ > 56 and you obtain a p-value of 0.001 (TO 3 DECIMALS) and the result is not significant.b.You test Ho: µ > = 56 versus Ha: µ < 56 and you obtain a p-value of 0.001 (TO 3 DECIMALS) and the result is not significant.c.You test Ho: µ <= 56 versus Ha: µ > 56 and you obtain a pvalue of 0.001 (TO 3 DECIMALS) and the result is significant.d.You test Ho: µ <= 56 versus Ha: µ > 56 and you obtain a p-value of 0.001 (TO 3 DECIMALS) and the result is not significant.

Solution: Given information: n=100 Sample size x= 57.5 Sample mean μ=56 Population mean σ=5…

Answered: random sample of 100 students is taken…

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 random sample of 100 students is taken from a larger population of students in a multi-lecture course and the sample mean (average) of their final grades is found to be 57.5. Suppose it is known that the population standard deviation is 5. Use R to help you test, with a significance level of 0.01, whether there is significant evidence that the average grade for the population exceeds 56. Choose the most correct statement.

You test Ho: µ < 56 versus Ha: µ > 56 and you obtain a p-value of 0.001 (TO 3 DECIMALS) and the result is not significant.

You test Ho: µ > = 56 versus Ha: µ < 56 and you obtain a p-value of 0.001 (TO 3 DECIMALS) and the result is not significant.

You test Ho: µ <= 56 versus Ha: µ > 56 and you obtain a pvalue of 0.001 (TO 3 DECIMALS) and the result is significant.

You test Ho: µ <= 56 versus Ha: µ > 56 and you obtain a p-value of 0.001 (TO 3 DECIMALS) and the result is not significant.

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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