Douglas is a farmer who believes that his cow produces an average of 7 gallons of milk per day. To test this, he randomly selects 31 days and records the number of gallons the cow produces on each of those days. The sample mean is 6.9 gallons with a sample standard deviation of 0.3 gallon. If the test statistic t=−1.86 and the alternative hypothesis is Ha:μ≠7, find the p-value range for the appropriate hypothesis test.Probability0.100.050.0250.010.005Degrees of Freedom 301.3101.6972.0422.4572.750311.3091.6962.0402.4532.744321.3091.6942.0372.4492.738331.3081.6922.0352.4452.733341.3071.6912.0322.4412.728351.3061.6902.0302.4382.724361.3061.6882.0282.4342.719371.3051.6872.0262.4312.715381.3041.6862.0242.4292.712391.3041.6852.0232.4262.708 Select the correct answer below: A) p-value >0.20B) 0.10< p-value <0.20C) 0.05< p-value <0.10D) 0.02< p-value <0.05

The aim is to find the range of p-value.

Answered: Douglas is a farmer who believes that…

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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Douglas is a farmer who believes that his cow produces an average of 7 gallons of milk per day. To test this, he randomly selects 31 days and records the number of gallons the cow produces on each of those days. The sample mean is 6.9 gallons with a sample standard deviation of 0.3 gallon. If the test statistic t=−1.86 and the alternative hypothesis is Ha:μ≠7, find the p-value range for the appropriate hypothesis test.

Probability	0.10	0.05	0.025	0.01	0.005
Degrees of Freedom
30	1.310	1.697	2.042	2.457	2.750
31	1.309	1.696	2.040	2.453	2.744
32	1.309	1.694	2.037	2.449	2.738
33	1.308	1.692	2.035	2.445	2.733
34	1.307	1.691	2.032	2.441	2.728
35	1.306	1.690	2.030	2.438	2.724
36	1.306	1.688	2.028	2.434	2.719
37	1.305	1.687	2.026	2.431	2.715
38	1.304	1.686	2.024	2.429	2.712
39	1.304	1.685	2.023	2.426	2.708

Select the correct answer below:

A) p-value >0.20

B) 0.10< p-value <0.20

C) 0.05< p-value <0.10

D) 0.02< p-value <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 + ...

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