# A confidence interval for your random heights

(5pts)

In this problem, we're going to return to our fun web program that generates random CSV data for people. Recall that you can access it via Python like so:

```
%matplotlib inline
import pandas as pd
df = pd.read_csv('https://www.marksmath.org/cgi-bin/random_data.csv?username=mark')
df.tail()
```

first_name | last_name | age | sex | height | weight | income | activity_level | |
---|---|---|---|---|---|---|---|---|

0 | Donna | Dinan | 35 | female | 65.37 | 164.26 | 1947 | high |

1 | Antonia | Davis | 39 | female | 64.95 | 140.40 | 2188 | none |

2 | Stephanie | Buss | 30 | female | 60.75 | 181.83 | 18108 | high |

3 | Wendell | Elmore | 26 | male | 64.68 | 157.90 | 1935 | moderate |

4 | Nina | Mcilhinney | 21 | female | 59.94 | 163.38 | 5675 | none |

Also recall that the data is randomly generated but the random number generator is seeded using the `username`

query parameter in the URL. Thus, if I execute that command several times, I get the same result every time. That result depends upon the `username`

, however. Thus, if you do it with your forum `username`

, you'll get a different result. Thus, we all have our own randomly generated data file!

*The problem*: Using the code above with your `username`

, generate your data file and then

- Compute the average value of the heights in your data (which you've done before),
- the standard deviation of the heights in your data,
- the standard error of the heights in your data,
- the margin of error to use the heights in your data to compute a $(100-s)\%$ confidence interval (where $s$ is your special number), and
- the resulting $(100-s)\%$ confidence interval for height

Be sure to include both the code that you typed, as well as the results in your post.

## Comments

%matplotlib inline

import pandas as pd

df = pd.read_csv('https://www.marksmath.org/cgi-bin/random_data.csv?username=jordan')

df.tail()

heights=df.height.sample(100,random_state=1)

xbar=heights.mean()

xbar

%66.73939999999997%

s= heights.std()

s

%4.122285043492017%

se = s/sqrt(100)

se = (s/10)

se

%0.41222850434920166%

from scipy.stats import norm

z=norm.ppf(0.045)

z

%-1.6953977102721358%

from scipy.stats import norm

z= norm.ppf(0.995)

z

%2.5758293035489004%

me= z*se

me

%1.061830261260809%

ci= [m-me, m+me]

ci

%[177.91816973873918, 180.0418302612608]%

1) Avg Values

65.55482) Std Deviation

4.1138766106528723) Std Error

0.41138766106528724) Margin of Error

z = -1.6953977102721358

zstr=-z

zstr

zstr=1.6953977102721358

0.69746569860429745) Confidence Interval for 91%

[64.8573343013957, 66.2522656986043]mean: 66.3

sd: 3.89

se: .39

margin of error: .79

z*: 2.05

confidence interval for 96%: (65.51,67.09)

Code for my data table:

1.) Average Value of the Heights:

= 66.30110000000002

2.) Standard Deviation of the Heights:

= 3.7302560084917624

3.) Standard Error of the Heights:

= 0.37302560084917624

4.) Margin of Error:

= 0.7460512016983525

5.) Confidence Interval for Height:

= [65.55504879830167, 67.04715120169837]

6.) z* Multiplier:

I had a 94% CI, so my number was 6

= 1.880793608151251

1.

m= 66.20770000000003

2.

s= 3.490168255907652

3.

se= 0.3490168255907652

5.

ci= [65.30869223321172, 67.10670776678835]

First, I'll import my data and compute my mean and standard deviation:

[66.49599999999998, 3.9782326922309807]

Thus, my standard error is:

0.39782326922309807

and my %z^*%-multiplier is 1.96 since:

-1.9599639845400545

1.) Mean:

65.35810000000001

2.) Standard Deviation:

3.701679306324183

3.) Standard error

0.37016793063241826

4.) Margin of error

0.7403358612648365

5.) Confidence Interval

[64.61776413873517, 66.09843586126485]

mean=67.02449999999999

standard deviation=3.8097767306462633

standard error=0.3809776730646263

0.9619022326935374

z*=1.7732002261111544

Margin of Error=0.6755496960214968

Confidence Interval=[66.3489503039785, 67.70004969602148]

This is the code importing my data along with the

meanandstandard deviation:[65.81690000000002, 3.854679615661196]The

standard erroris:0.3854679615661196The

z multiplieris:2.2-2.1700903775845606The

margin of erroris:0.8480295154454632The

confidence intervalis:[64.96887048455456, 66.66492951544548]1+2) mean and standard deviation

[66.81249999999999, 4.248674273324336]

3) standard deviation

0.4248674273324336

4) margin of error

0.8497348546648672

5) confidence interval

[65.96276514533511, 67.66223485466486]