Question

# 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

Verified
Step 1
1 of 6

Given:

\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*}

## Recommended textbook solutions #### Statistics for Business and Economics

11th EditionISBN: 9780324783254 (13 more)David R. Anderson, Dennis J. Sweeney, Thomas A. Williams
2,223 solutions #### Statistics

4th EditionISBN: 9780393929720 (3 more)Freedman, Robert Pisani, Roger Purves
1,001 solutions #### The Practice of Statistics for the AP Exam

5th EditionISBN: 9781464108730 (2 more)Daniel S. Yates, Daren S. Starnes, David Moore, Josh Tabor
2,433 solutions #### Statistics and Probability with Applications

3rd EditionISBN: 9781464122163Daren S. Starnes, Josh Tabor
2,555 solutions