You may need to use the appropriate appendix table or technology to answer this question. You are given the following information obtained from a random sample of 4 observations. 24 46 31 55 You want to determine whether or not the mean of the population from which this sample was taken is significantly different from 48. (Assume the population is normally distributed.) (a) State the null and the alternative hypotheses. (Enter != for ≠ as needed.) H0: Ha: (b) Determine the test statistic. (Round your answer to three decimal places.) (c) Determine the p-value, and at the 5% level of significance, test to determine whether or not the mean of the population is significantly different from 48. Find the p-value. (Round your answer to four decimal places.) p-value = State your conclusion. Do not reject H0. There is sufficient evidence to conclude that the mean of the population is different from 48.Reject H0. There is insufficient evidence to conclude that the mean of the population is different from 48. Do not reject H0. There is insufficient evidence to conclude that the mean of the population is different from 48.Reject H0. There is sufficient evidence to conclude that the mean of the population is different from 48

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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You may need to use the appropriate appendix table or technology to answer this question.

You are given the following information obtained from a random sample of 4 observations.

You want to determine whether or not the mean of the population from which this sample was taken is significantly different from 48. (Assume the population is normally distributed.)

(a)

State the null and the alternative hypotheses. (Enter != for ≠ as needed.)

H₀:

H_a:

(b)

Determine the test statistic. (Round your answer to three decimal places.)

(c)

Determine the p-value, and at the 5% level of significance, test to determine whether or not the mean of the population is significantly different from 48.

Find the p-value. (Round your answer to four decimal places.)

p-value =

State your conclusion.

Do not reject H₀. There is sufficient evidence to conclude that the mean of the population is different from 48.Reject H₀. There is insufficient evidence to conclude that the mean of the population is different from 48. Do not reject H₀. There is insufficient evidence to conclude that the mean of the population is different from 48.Reject H₀. There is sufficient evidence to conclude that the mean of the population is different from 48.

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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