A manufacturer of chocolate candies uses machines to package candies as they move along a filling line. Although the packages are labeled as 8 ounces, the company wants the packages to contain a mean of8.17ounces so that virtually none of the packages contain less than 8 ounces. A sample of50packages is selected periodically, and the packaging process is stopped if there is evidence that the mean amount packaged is different from8.17ounces. Suppose that in a particular sample of50packages, the mean amount dispensed is8.161ounces, with a sample standard deviation of0.048ounce. Complete parts (a) and (b).Click here to view page 1 of the critical values for the t Distribution.LOADING...Click here to view page 2 of the critical values for the t Distribution.LOADING...a. Is there evidence that the population mean amount is different from8.17ounces? (Use a0.10level of significance.)Find the critical values of the t distributionDetermine the p-value and interpret its meaning.

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Description: A manufacturer of chocolate candies uses machines to package candies as they move along a filling line. Although the packages are labeled as 8 ounces, the company wants the packages to contain a mean of8.17ounces so that virtually none of the packag

Given Information: μ=8.17 Sample size (n) = 50 Sample mean (x¯) = 8.161 Sample standard deviation (s) = 0.048 Significance level α=0.10 To test if the population mean amount is different from 8.17 ounces: State the Hypothesis as follows: Null Hypothesis: H0:μ=8.17 Alternative Hypothesis: H1:μ≠8.17 Test statistic is given by the formula: t=x¯-μsn Substitute the given values in the formula: t=8.161-8.170.04850=-0.0090.00679≈-1.325 Thus, the value of the test statistic is -1.325 Degrees of freedom df=n-1=50-1=49 For a two tailed test, critical values at 0.10 significance level and 49 degrees of freedom are: -1.6766 and +1.6766 Since, the computed value of the test statistic lies between the two critical values, we fail to reject the null hypothesis at 0.10 significance level. P-value is the probability of obtaining the value of the test statistic or more extreme, assuming the null hypothesis is true. Compute the p-value for the two tailed test using Excel function "=TDIST(t, degrees of freedom, 2-tailed)" P-value obtained is 0.19132 Since, p-value is greater than the significance level(0.10), we fail to reject the null hypothesis. There is no sufficient evidence to conclude that the population mean amount is different from 8.17 ounces.

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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A manufacturer of chocolate candies uses machines to package candies as they move along a filling line. Although the packages are labeled as 8 ounces, the company wants the packages to contain a mean of

8.17

ounces so that virtually none of the packages contain less than 8 ounces. A sample of

packages is selected periodically, and the packaging process is stopped if there is evidence that the mean amount packaged is different from

8.17

ounces. Suppose that in a particular sample of

packages, the mean amount dispensed is

8.161

ounces, with a sample standard deviation of

0.048

ounce. Complete parts (a) and (b).

Click here to view page 1 of the critical values for the t Distribution.

Click here to view page 2 of the critical values for the t Distribution.

a. Is there evidence that the population mean amount is different from

8.17

ounces? (Use a

0.10

level of significance.)

Find the critical values of the t distribution

Determine the p-value and interpret its meaning.

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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