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.
failed

Solution

failed
failed

Solution Steps

Step 1: Calculate the Mean

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

\[ \mu = \frac{\sum_{i=1}^N x_i}{N} \]

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

\[ \mu = \frac{272}{8} = 34.0 \]

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

Step 2: Calculate the Variance

The variance is calculated using the formula:

\[ \sigma^2 = \frac{\sum (x_i - \mu)^2}{n-1} \]

Substituting the values, we find:

\[ \sigma^2 = 214.0 \]

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

Step 3: Calculate the Standard Deviation

The standard deviation is the square root of the variance:

\[ \sigma = \sqrt{214.0} \approx 14.63 \]

Thus, the standard deviation of the number of ants is \( \sigma \approx 14.63 \).

Final Answer

The mean number of ants is \( \mu = 34.0 \), the variance is \( \sigma^2 = 214.0 \), and the standard deviation is \( \sigma \approx 14.63 \).

\[ \boxed{\mu = 34.0, \sigma^2 = 214.0, \sigma \approx 14.63} \]

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
When does cytokinesis begin?
failedAnswered
Why did the Council of Trent issue this message about Renaissance art needing to be more modest during its 25th session in 1563? It was trying to require Catholics to worship religious art rather than the holy people who were portrayed in it. It was trying to suppress the degree of sexuality featured in religious works of art done by Northern Renaissance artists. It was trying to keep wealthy patrons from withdrawing their financial support to Italian artists. It was trying to prevent Catholics from converting to Protestantism.
failedAnswered
Write an equation of the line passing through point P(0,1) that is parallel to the line y=-2x+3. An equation is:
failedAnswered
The floor of a rectangular meeting room has a raised platform that is the same length as the room and is 1/6 the width of the room. Part A What is the width of the raised platform? Write an equation to model your work. Part B Estimate the area of the floor, including the raised platform.
failedAnswered
Proactive recruiting does not consist of the following: 1 Point(s) Code red situation with increased stress and costing more money Anticipating the staffing need of a business and recruiting accordingly Analyzing metrics Setting target dates to ensure staffing needs are met Planning for no shows to ensure adequate staffing