## Related questions with answers

A coin is tossed 500 times. True or false, and explain. a) The SE for the percentage of heads among the 500 tosses is 2.2 percentage points. b) The SE for the percentage of tails among the 500 tosses is 2.2 percentage points. c) The SE for the difference

$\begin{array} { c } { \text { percentage of heads - percentage of tails } } \\ { \text { is } \sqrt { 2.2 ^ { 2 } + 2.2 ^ { 2 } } \approx 3.1 \text { percentage points. } } \end{array}$

Solution

VerifiedGiven:

$\begin{align*} \text{Sample size}&=500 \end{align*}$

(a) Let 0 represent tails and let 1 represent heads.

Since we expect heads and tails to be equally likely to occur by chance, we use a box containing a single 0 and a single 1.

Next, we determine the standard deviation of the values in the box. The standard deviation is the square root of the squared deviations from the mean divided by the sample size decreased by 1:

$\begin{align*} \text{SD box}&=\sqrt{\frac{\begin{matrix}(0-0.5)^2+(1-0.5)^2\end{matrix}}{2}} \\ &=\sqrt{\frac{\begin{matrix}(-0.5)^2+0.5^2\end{matrix}}{2}} \\ &=\sqrt{\frac{\begin{matrix}0.25+0.25\end{matrix}}{2}} \\ &=\sqrt{\frac{\begin{matrix}0.5\end{matrix}}{2}} \\ &=\sqrt{0.25} \\ &=0.5 \end{align*}$

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