A scientist for a company that manufactures fabric wants to assess the percentage of polyester in the fabric.
The advertised percentage is 15%. The scientist measures the percentage of polyester in 20 random samples.
Previous measurements found that the population standard deviation is 2.6%.
Sample Id 
Percent Polyester 
1 
15.2 
2 
12.4 
3 
15.4 
4 
16.5 
5 
15.9 
6 
17.1 
7 
16.9 
8 
14.3 
9 
19.1 
10 
18.2 
11 
18.5 
12 
16.3 
13 
20.0 
14 
19.2 
15 
12.3 
16 
12.8 
17 
17.9 
18 
16.3 
19 
18.7 
20 
16.2 
from scipy.stats import norm
import pandas as pd
import math
dataset = pd.Series([15.2, 12.4, 15.4, 16.5, 15.9, 17.1, 16.9, 14.3, 19.1, 18.2, 18.5, 16.3, 20, 19.2, 12.3, 12.8, 17.9, 16.3, 18.7, 16.2])
alpha = 0.05
mean = dataset.mean()
mu = 15
sigma = 2.6
n = dataset.size
z = (mean  mu) / (sigma / math.sqrt(n))
p = norm.sf(abs(z))*2
print('z =', z)
print('p =',p)
z = 2.5112763439613035 p = 0.012029548638074252
The table presents data from two jeans factories. In each of the columns is presented the monthly number of defective products.
The data for factory 1 are for 10 months, and for factory 2  for 12 months.
Is there a difference in the average number of defective products in the two factories?
Factory 1 
Factory 2 
80 
79 
76 
73 
70 
72 
80 
62 
66 
76 
85 
68 
79 
70 
71 
86 
81 
75 
76 
68 
73 

66 
from scipy import stats
factory1 = pd.Series([80, 76, 70, 80, 66, 85, 79, 71, 81, 76])
factory2 = pd.Series([79, 73, 72, 62, 76, 68, 70, 86, 75, 68, 73, 66])
stats.ttest_ind(factory1, factory2)
Ttest_indResult(statistic=1.5519317588776553, pvalue=0.1363596260157604)