a. Calculate the SE for estimating the mean sugar content of cereals displayed on the lower shelves, using data only from the lower shelves (ignoring the other two samples), and explain what the number means.b. Calculate the same SE as above, except use data from all observations, not just the 20 from the lower shelves. Which SE is better?c. Can we conclude that on average cereals displayed on the middle shelves contain more than 2 gr/serving sugar compared to the cereals displayed on the lower shelves? Test at α = 0.05. Clearly define the parameters and the hypotheses, report the test statistic and p-value. Summary Statistics for SugarsShelf Count Average Standard deviation Minimum Maximum204.854.51051152219.61905 4.128881513366.52778 3.8358214Total 776.93506 4.4228415The StatAdvisorThis table shows various statistics for Sugars for each of the 3 levels of Shelf. The one-way analysis of variance is primarilyintended to compare the means of the different levels, listed here under the Average column. Select Means Plot from the list ofGraphical Options to display the means graphically. ANOVA TableSourceSum of Squares Df Mean Square F-Ratio P-ValueBetween groups|244.2012 122.17.270.001374 16.7902Within groups 1242.47Total (Corr.)1486.6876The StatAdvisorThe ANOVA table decomposes the variance of Sugars into two components: a between-group component and a within-groupcomponent. The F-ratio, which in this case equals 7.27212, is a ratio of the between-group estimate to the within-group estimateSince the P-value of the F-test is less than 0.05, there is a statistically significant difference between the mean Sugars from onelevel of Shelf to another at the 95% significance level.

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Description: a. Calculate the SE for estimating the mean sugar content of cereals displayed on the lower shelves, using data only from the lower shelves (ignoring the other two samples), and explain what the number means.b. Calculate the same SE as above, except

The summary statistics given is Solution for parts (a), (b), (c) is given below.

Answered: a. Calculate the SE for estimating the…

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a. Calculate the SE for estimating the mean sugar content of cereals displayed on the lower shelves, using data only from the lower shelves (ignoring the other two samples), and explain what the number means.

b. Calculate the same SE as above, except use data from all observations, not just the 20 from the lower shelves. Which SE is better?

c. Can we conclude that on average cereals displayed on the middle shelves contain more than 2 gr/serving sugar compared to the cereals displayed on the lower shelves? Test at α = 0.05. Clearly define the parameters and the hypotheses, report the test statistic and p-value.

Summary Statistics for Sugars
Shelf Count Average Standard deviation Minimum Maximum
20
4.85
4.51051
15
2
21
9.61905 4.12888
15
13
36
6.52778 3.83582
14
Total 77
6.93506 4.42284
15
The StatAdvisor
This table shows various statistics for Sugars for each of the 3 levels of Shelf. The one-way analysis of variance is primarily
intended to compare the means of the different levels, listed here under the Average column. Select Means Plot from the list of
Graphical Options to display the means graphically.

ANOVA Table
Source
Sum of Squares Df Mean Square F-Ratio P-Value
Between groups|244.201
2 122.1
7.27
0.0013
74 16.7902
Within groups 1242.47
Total (Corr.)
1486.68
76
The StatAdvisor
The ANOVA table decomposes the variance of Sugars into two components: a between-group component and a within-group
component. The F-ratio, which in this case equals 7.27212, is a ratio of the between-group estimate to the within-group estimate
Since the P-value of the F-test is less than 0.05, there is a statistically significant difference between the mean Sugars from one
level of Shelf to another at the 95% significance level.

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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