A heavy hypothesis test

mark

(5 pt)

Our CDC data set has just over 1000 men who are 5'9''. We can pack them into a data frame and take a sample of size 100 from that data frame as follows:

import pandas as pd

df = pd.read_csv('https://www.marksmath.org/data/cdc.csv')
df_men = df[df.gender=='m']
five9 = df_men[df_men.height==69]
sample = five9.sample(100, random_state=5)
print(len(five9))
sample.head()

	genhlth	exerany	hlthplan	smoke100	height	weight	wtdesire	age	gender
838	excellent	1	1	1	69	160	160	31	m
13979	good	1	1	1	69	150	165	52	m
16025	fair	1	1	1	69	190	150	53	m
14550	excellent	1	1	0	69	200	180	29	m
4765	fair	0	1	1	69	235	180	56	m

The CDC recommends that the average weight of men at this height be 165 points, but we suspect that it might be more.

Your exercise is to use the code above (with your special number as the random_state to grab a sample of size 100 and test the null hypothesis that the average weight of men at 5'9'' is 165 vs the alternative hypothesis that the actual mean is larger.

Thus, my alternative hypothesis is:

%H_A: mu > 165%

sarah

%H_0: mu = 165%
%H_A: mu > 165%

With 95% level of confidence
Therefore a=0.05

import pandas as pd
import numpy as np
from scipy.stats import norm

df = pd.read_csv('https://www.marksmath.org/data/cdc.csv')
df_men = df[df.gender=='m']
five9 = df_men[df_men.height==69]
sample = five9.sample(100, random_state=9)
print(len(five9))
sample.head()

m=sample.weight.mean()
s=sample.weight.std()
se=s/np.sqrt(100)
[m,s,se]

[176.33, 23.76486456680929, 2.376486456680929]

z = (m-165)/se
z

4.767542423037337

norm.cdf(-z)

9.324336787626066e-07

At a 95% confidence level

9.324336787626066e-07 < 0.05

Therefore, we reject the null hypothesis

alex

Hypotheses:

%H_0: mu=165%

%H_A: mu>165%

Data Set:

import pandas as pd

df = pd.read_csv('https://www.marksmath.org/data/cdc.csv')
df_men = df[df.gender=='m']
five9 = df_men[df_men.height==69]
sample = five9.sample(100, random_state=1)
print(len(five9))
sample.head()

Mean:

m= df.weight.mean()
m

=169.68295

Standard Deviation:

sd= df.weight.std()
sd

=40.080969967120254

Standard Error:

se= sd/np.sqrt(100)
se

=4.008096996712025

Z Score:

z= (m-165)/se
z

=1.1683724230829704

P Value:

%P(Z=1.16)= 0.123%

%P Value (0.123) > Confidence Level (.05)%

So, we fail to reject %H_A%

ben

import pandas as pd

df = pd.read_csv('https://www.marksmath.org/data/cdc.csv')
df_men = df[df.gender=='m']
five9 = df_men[df_men.height==69]
sample = five9.sample(100, random_state=4)
print(len(five9))
sample.head()

mean:

df.weight.mean()

=169.68296

standard deviation

df.weight.std()

=40.080969967120254

standard error

se = sd/np.sqrt(100)
se

=4.008

Z score

z = (m-165)/se
z

=1.167

%H_0:mu=165%
%H_A:mu>165%

P value:
P(Z=1.16)=.13
Pvalue(.13)>(.05)

we fail to reject %H_A%

isabel

%H_A:mu=165%
%H_A:mu>165%

Mean, Standard Deviation, Population

weight = df.weight
m = weight.mean()
s = weight.std()
n = len(weight)
[m,s,n]

[169.68295, 40.080969967120254, 20000]

Standard Error

se = s/10
se

4.008096996712025

Z Score

z= (m-165)/se
z

1.1683724230829704

%P(Z=1.17)=.1210%

PValue(.1210) > Confidence Level (.05)

So, we fail to reject %H_A%

zach

import pandas as pd

from scipy.stats import norm

from numpy import sqrt

df = pd.read_csv('https://www.marksmath.org/data/cdc.csv')
df_men = df[df.gender=='m']
five9 = df_men[df_men.height==69]
sample = five9.sample(100, random_state=10)
print(len(five9))
sample.head()

import numpy as np

With a 95% level of confidence, our alpha value equals 0.05

m = np.mean([160, 150, 170, 180, 160])
m

mean=164

s = np.std([160, 150, 170, 180, 160])
s

standard deviation=10.198039027185569

se = s/sqrt(100)
se

standard error=1.0198039027185568

z = (m-165)/se
z

z-score=-0.9805806756909203

probability value=0.1635

p-value (0.8365) > confidence level (0.05)

Therefore, we fail to reject the null hypothesis.

%H_0: mu = 165%
%H_A: mu < 165%

Beau

%H_0: mu=165%
%H_A: mu>165%

Data Set imported from:

    import pandas as pd

    df = pd.read_csv('https://www.marksmath.org/data/cdc.csv')
    df_men = df[df.gender=='m']
    five9 = df_men[df_men.height==69]
    sample = five9.sample(100, random_state=3)
    print(len(five9))
    sample.head()

The Mean and Standard Deviation are:

s = df.weight.std()
m = df.weight.mean()
[m,s]

[169.68295, 40.080969967120254]

The Standard Error is:

se = s/x
se

4.008096996712025

The Z score is: 1.683 with a Probability of 0.8790 .

P value is: (1-0.8790)= 0.121

P = 0.121 > 0.05, therefore I fail to reject the null hypothesis.

jordan

import pandas as pd

df = pd.read_csv('https://www.marksmath.org/data/cdc.csv')
df_men = df[df.gender=='m']
five9 = df_men[df_men.height==69]
sample = five9.sample(100, random_state=7)
print(len(five9))
sample.head()

Mean:
sample.weight.mean()
m
%178.98%

Standard Deviation:
sample.weight.std()
sd
%25.36599967267088%

Standard Error:
se=2.53659
se
%2.53659%

z score:
z=(m-165)/se
z
%5.511336085059072%

%H_A:mu>165%
%H_O:mu=165%
Thus, I reject the null hypothesis.

ashley

Hypothesis:
%H_0:mu=165%
%H_A:mu>165%

Data set:

import pandas as pd

df = pd.read_csv('https://www.marksmath.org/data/cdc.csv')
df_men = df[df.gender=='m']
five9 = df_men[df_men.height==69]
sample = five9.sample(100, random_state=5)
print(len(five9))
sample.head()

Mean:

m= df.weight.mean()
m

=169.68295

Standard Deviation:

sd= df.weight.std()
sd

=40.080969967120254

Standard Error:

m=sample.weight.mean()
se=sample.wieght.std()/(10)

=[180.77, 2.9344300635693807]

Margin of Eroor

me=2*se
me

=5.8688601271387615

Z score:

z=(m-165)/se
z

=5.374127056488

The Z-score is 5.374127056488, therefore we can reject the null.