Questions: Ants on a Sandwich How many ants will climb on a piece of a peanut butter sandwich left on the ground near an ant hill? To study this, a student in Australia left a piece of a sandwich for several minutes, then covered it with a jar and counted the number of ants. He did this eight times, and the results are shown in Table 1. (In fact, he also conducted an experiment to see if there is a difference in number of ants based on the sandwich filling.) Number of ants: 43, 59, 22, 25, 36, 47, 19, 21 Table 1 Number of ants on a sandwich Margaret M., "Favourite Experiments: An Addendum to What is the Use of Experiments Conducted by Statistics Students?," Journal of Statistics Education, 1994, http://www.amstat.org/publications/jse/v2n1/mackisack.supp.html.

Ants on a Sandwich How many ants will climb on a piece of a peanut butter sandwich left on the ground near an ant hill? To study this, a student in Australia left a piece of a sandwich for several minutes, then covered it with a jar and counted the number of ants. He did this eight times, and the results are shown in Table 1. (In fact, he also conducted an experiment to see if there is a difference in number of ants based on the sandwich filling.) Number of ants: 43, 59, 22, 25, 36, 47, 19, 21 Table 1 Number of ants on a sandwich Margaret M., "Favourite Experiments: An Addendum to What is the Use of Experiments Conducted by Statistics Students?," Journal of Statistics Education, 1994, http://www.amstat.org/publications/jse/v2n1/mackisack.supp.html.
Transcript text: Section 3.3 Hon Question 6 of 9 MATH 227 Zoom $\quad x \mid$ START HERE - H STARCHERE:H $\times 2.1$ Homework https://education.wiley.com/was/ui/v2/assessment-player/index.html?launchld=0067325f-57ab-4601-a4ef-293b04267b07\#/question/5 Section 3.3 Homework: Constructing Bootstrap Confidence Intervals Question 6 of 9 $3.5 / 4$ Ants on a Sandwich How many ants will climb on a piece of a peanut butter sandwich left on the ground near an ant hill? To study this, a student in Australia left a piece of a sandwich for several minutes, then covered it with a jar and counted the number of ants. He did this eight times, and the results are shown in Table 1. (In fact, he also conducted an experiment to see if there is a difference in number of ants based on the sandwich filling.) ${ }^{1}$ \begin{tabular}{llllllllll} \hline \begin{tabular}{l} Number of \\ ants \end{tabular} & 43 & 59 & 22 & 25 & 36 & 47 & 19 & 21 \\ \hline \end{tabular} Table 1 Number of ants on a sandwich ${ }^{1}$ Margaret M., "Favourite Experiments: An Addendum to What is the Use of Experiments Conducted by Statistics Students?," Journal of Statistics Education, 1994, http://www.amstat.org/publications/jse/v2n1/mackisack.supp.html.
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Solution

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Solution Steps

Step 1: Calculate the Mean

To find the mean number of ants, we use the formula:

μ=∑i=1NxiN \mu = \frac{\sum_{i=1}^N x_i}{N}

where N N is the number of observations and xi x_i are the individual observations. For our data:

μ=2728=34.0 \mu = \frac{272}{8} = 34.0

Thus, the mean number of ants is μ=34.0 \mu = 34.0 .

Step 2: Calculate the Variance

The variance is calculated using the formula:

σ2=∑(xi−μ)2n−1 \sigma^2 = \frac{\sum (x_i - \mu)^2}{n-1}

Substituting the values, we find:

σ2=214.0 \sigma^2 = 214.0

Therefore, the variance of the number of ants is σ2=214.0 \sigma^2 = 214.0 .

Step 3: Calculate the Standard Deviation

The standard deviation is the square root of the variance:

σ=214.0≈14.63 \sigma = \sqrt{214.0} \approx 14.63

Thus, the standard deviation of the number of ants is σ≈14.63 \sigma \approx 14.63 .

Final Answer

The mean number of ants is μ=34.0 \mu = 34.0 , the variance is σ2=214.0 \sigma^2 = 214.0 , and the standard deviation is σ≈14.63 \sigma \approx 14.63 .

μ=34.0,σ2=214.0,σ≈14.63 \boxed{\mu = 34.0, \sigma^2 = 214.0, \sigma \approx 14.63}

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