A soft-drink manufacturer claims that its 12-ounce cans contain, on average, different from 65 calories. A random sample of 21 cans of this soft drink, which were checked for calories, contained a mean of 72 calories with a sample standard deviation of 5 calories. Assume that the distribution of the calories of the soft drink is normally distributed. Use 1% significance level to determine that the mean calories in the soft drink is different from 30 calories. Answer the following questions. Identify the claim and state the H0 and H1.Find the critical value.Calculate the test statistic.Calculate the p-value.Make a decision to reject or fail to reject the H0.Interpret the decision in the context of the original claim.

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Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 7PPS

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A soft-drink manufacturer claims that its 12-ounce cans contain, on average, different from 65 calories. A random sample of 21 cans of this soft drink, which were checked for calories, contained a mean of 72 calories with a sample standard deviation of 5 calories. Assume that the distribution of the calories of the soft drink is normally distributed. Use 1% significance level to determine that the mean calories in the soft drink is different from 30 calories. Answer the following questions.

Identify the claim and state the H₀ and H₁.
Find the critical value.
Calculate the test statistic.
Calculate the p-value.
Make a decision to reject or fail to reject the H₀.
Interpret the decision in the context of the original claim.

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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