The average weight of a package of rolled oats is supposed to be at least 15 ounces. A sample of 18 packages shows a mean of 14.82 ounces with a standard deviation of 0.50 ounce. (a) At the 5 percent level of significance, is the true mean smaller than the specification? Clearly state your hypotheses and decision rule. H0: μ ≥ 15. Reject H0 if tcalc > –1.740H1: μ < 15. Reject H1 if tcalc < –1.740H0: μ ≥ 15. Reject H0 if tcalc < –1.740H1: μ < 15. Reject H1 if tcalc > –1.740 multiple choice 1abcd (b) If α = .010, we would have failed to reject the null hypothesis.rejected the null hypothesis. multiple choice 2ab (c) Use Excel to find the p-value. (Round your answer to 4 decimal places.)

Solution: Given information: n= 18 Sample size x =14.82 Sample mean s= 0.50 Sample standard…

Answered: The average weight of a package of…

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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The average weight of a package of rolled oats is supposed to be at least 15 ounces. A sample of 18 packages shows a mean of 14.82 ounces with a standard deviation of 0.50 ounce.

(a) At the 5 percent level of significance, is the true mean smaller than the specification? Clearly state your hypotheses and decision rule.

H₀: μ ≥ 15. Reject H₀ if t_calc > –1.740
H₁: μ < 15. Reject H₁ if t_calc < –1.740
H₀: μ ≥ 15. Reject H₀ if t_calc < –1.740
H₁: μ < 15. Reject H₁ if t_calc > –1.740

multiple choice 1

(b) If α = .010, we would have

failed to reject the null hypothesis.
rejected the null hypothesis.

multiple choice 2

(c) Use Excel to find the p-value. (Round your answer to 4 decimal places.)

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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