Question

how to calculate standard error of mean. suppose you have two data - sets for the number of hummingbirds that visited two feeders. one feeder was located in an open field (site a), the other feeder was located in a wooded area (site b). researchers recorded the number of hummingbirds at a feeder each day over a period of 4 days. question: do hummingbirds have a preference for a feeding location? null hypothesis: hummingbirds do not have a preference for the feeding location across sites. data. site a: 6, 8, 6, 8; site b: 4, 6, 8, 14. step 1: calculate the standard deviation (sd) for both data sets. x = each value, $\bar{x}$ = mean, n = sample size. $sd=sqrt{\frac{sum(x - \bar{x})^2}{n - 1}}$. site a: $sdapprox1.15$. site b: $sdapprox4.32$. step 2: calculate the standard error for both data sets. $se_1=\frac{s}{sqrt{n}}$, n = sample size, s = standard deviation. step 3: create a bar graph showing the error bar for both data sets. include: title, x and y axis labels, error bar ($pm2se$). step 4: summarize data in a caption that explain the graphed data. # of birds. feeding location. day 5

Explanation:

Step 1: Calculate the mean for each site

For Site A: $\bar{x}_A=\frac{6 + 8+6 + 8+7}{5}=\frac{35}{5} = 7$
For Site B: $\bar{x}_B=\frac{4+6 + 8+14+8}{5}=\frac{40}{5}=8$

Step 2: Calculate the standard - deviation (SD) for each site

For Site A:
First, calculate $(x - \bar{x})^2$ values:
$(6 - 7)^2=1$, $(8 - 7)^2 = 1$, $(6 - 7)^2=1$, $(8 - 7)^2 = 1$, $(7 - 7)^2=0$
$\sum(x-\bar{x})^2=1 + 1+1 + 1+0 = 4$
$SD_A=\sqrt{\frac{\sum(x - \bar{x})^2}{n - 1}}=\sqrt{\frac{4}{4}} = 1$

For Site B:
$(4 - 8)^2=16$, $(6 - 8)^2 = 4$, $(8 - 8)^2=0$, $(14 - 8)^2 = 36$, $(8 - 8)^2=0$
$\sum(x-\bar{x})^2=16 + 4+0 + 36+0 = 56$
$SD_B=\sqrt{\frac{\sum(x - \bar{x})^2}{n - 1}}=\sqrt{\frac{56}{4}}=\sqrt{14}\approx3.74$

Step 3: Calculate the standard error of the mean (SE) for each site

For Site A: $SE_A=\frac{SD_A}{\sqrt{n}}=\frac{1}{\sqrt{5}}\approx0.45$
For Site B: $SE_B=\frac{SD_B}{\sqrt{n}}=\frac{3.74}{\sqrt{5}}\approx1.67$

Step 4: Create a bar - graph

On the x - axis, label the two feeding locations (Site A and Site B). On the y - axis, label "Number of Hummingbirds". Draw two bars, one for Site A and one for Site B. The height of the bar represents the mean number of hummingbirds at each site. Above each bar, draw error bars representing $\pm SE$.

Answer:

The standard error of the mean for Site A is approximately $0.45$ and for Site B is approximately $1.67$.