Using the information in the picture, answer these questions Define the null and alternative hypotheses in mathematical terms as well as in words. Identify the level of significance. Include the test statistic and the P-value. See Step 2 in the Python script. (Note that Python methods return two tailed P-values. You must report the correct P-value based on the alternative hypothesis.)
Using the information in the picture, answer these questions Define the null and alternative hypotheses in mathematical terms as well as in words. Identify the level of significance. Include the test statistic and the P-value. See Step 2 in the Python script. (Note that Python methods return two tailed P-values. You must report the correct P-value based on the alternative hypothesis.)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Question
Using the information in the picture, answer these questions
- Define the null and alternative hypotheses in mathematical terms as well as in words.
- Identify the level of significance.
- Include the test statistic and the P-value. See Step 2 in the Python script. (Note that Python methods return two tailed P-values. You must report the correct P-value based on the alternative hypothesis.)
- Provide a conclusion and interpretation of the test: Should the null hypothesis be rejected? Why or why not?
![Step 1: Generating sample data
This block of Python code will generate two samples, both of size 50, that you will use in this discussion. The datasets will be unique to you and therefore your
answers will be unique as well. The numpy module in Python allows you to create a data set using a Normal distribution. The data sets will be saved in Python
dataframes and will be used in later calculations.
Click the block of code below and hit the Run button above.
import pandas as pd
import numpy as np
# create 50 randomly chosen values from a normal distribution. (arbitrarily using mean-2.48 and standard deviation-0.500)
diameters_sampled np.random.normal(2.48,0.588,50)
#convert the array into a dataframe with the column name "diameters" using pandas Library
diameters_sampled_df = pd.DataFrame(diameters_samplai, columns=["diameters'])
diameters_sample1_df = diameters_sample1_df.round(2)
# create 50 randomly chosen values from a normal distribution. (arbitrarily using mean-2.50 and standard deviation-0.758)
diameters_sample2 np.random.normal(2.58,0.758,50)
#convert the array into a dataframe with the column name "diameters" using pandas Library
pd.DataFrano(diameters_sample2, columns=["diameters'])
diameters_sample2 df
diameters_sample2_df = diameters_sample2_df.round(2)
# print the dataframe to see the first 5 observations (note that the index of dataframe starts at 8)
print("Diameters data frame of the first sample (showing only the first five observations)")
print(diameters_sample1_df.head())
print()
print("Diameters data frame of the second sample (showing only the first five observations)")
print(diameters_sample2_df.head())
Diameters data frame of the first sample (showing only the first five observations)
diameters
2.56
3.10
2.85
1
2
3
4
1.87
2.15
Diameters data frame of the second sample (showing only the first five observations)
diameters
2.44
2.27
3.88
1.34
2.78
1
2
3
Step 2: Performing hypothesis test for the difference in population proportions
The z-test for proportions can be used to test for the difference in proportions. The proportions_ztest method in statsmodels.stats.proportion submodule runs
this test. The input to this method is a list of counts meeting a certain condition (given in the problem statement) and a list of sample sizes for the two samples.
Counts Python list that is assigned the number of observations in each sample with diameter values less than 2.20.
Python list that is assigned the total number of observations in each sample.
Click the block of code below and hit the Run button above.
from statsmodels.stats.proportion import proportions_ztest
#number of observations in the first sample with diameter values Less than 2.20.
counti len(diameters_sample1_df[diameters_sample1_df["diameters']<2.20])
#number of observations in the second sample with diameter values Less than 2.28.
count2 len(diameters_sample2_df[diameters_sample2_df["diameters']<2.20])
#counts Python List
counts [counti, count2]
#number of observations in the first sample
ni len(diameters_sample1_df)
#number of observations in the second sample
n2 len(diameters_sample2_df)
#n Python List
n = [1, 2]
#perform the hypothesis test. output is a Python tuple that contains test_statistic and the two-sided P_value.
test_statistic, p_value proportions_ztest(counts, n)
print("test-statistic =*, round(test_statistic, 2))
print("two tailed p-value=", round(p_value,4))
test-statistic = 8.69
two tailed p-value - 0.4884](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc697cfa7-35be-400d-88d6-26bf90a0b862%2F226305fd-8f9a-4f10-aaef-8046c8d1636e%2Fsij7mhp_processed.png&w=3840&q=75)
Transcribed Image Text:Step 1: Generating sample data
This block of Python code will generate two samples, both of size 50, that you will use in this discussion. The datasets will be unique to you and therefore your
answers will be unique as well. The numpy module in Python allows you to create a data set using a Normal distribution. The data sets will be saved in Python
dataframes and will be used in later calculations.
Click the block of code below and hit the Run button above.
import pandas as pd
import numpy as np
# create 50 randomly chosen values from a normal distribution. (arbitrarily using mean-2.48 and standard deviation-0.500)
diameters_sampled np.random.normal(2.48,0.588,50)
#convert the array into a dataframe with the column name "diameters" using pandas Library
diameters_sampled_df = pd.DataFrame(diameters_samplai, columns=["diameters'])
diameters_sample1_df = diameters_sample1_df.round(2)
# create 50 randomly chosen values from a normal distribution. (arbitrarily using mean-2.50 and standard deviation-0.758)
diameters_sample2 np.random.normal(2.58,0.758,50)
#convert the array into a dataframe with the column name "diameters" using pandas Library
pd.DataFrano(diameters_sample2, columns=["diameters'])
diameters_sample2 df
diameters_sample2_df = diameters_sample2_df.round(2)
# print the dataframe to see the first 5 observations (note that the index of dataframe starts at 8)
print("Diameters data frame of the first sample (showing only the first five observations)")
print(diameters_sample1_df.head())
print()
print("Diameters data frame of the second sample (showing only the first five observations)")
print(diameters_sample2_df.head())
Diameters data frame of the first sample (showing only the first five observations)
diameters
2.56
3.10
2.85
1
2
3
4
1.87
2.15
Diameters data frame of the second sample (showing only the first five observations)
diameters
2.44
2.27
3.88
1.34
2.78
1
2
3
Step 2: Performing hypothesis test for the difference in population proportions
The z-test for proportions can be used to test for the difference in proportions. The proportions_ztest method in statsmodels.stats.proportion submodule runs
this test. The input to this method is a list of counts meeting a certain condition (given in the problem statement) and a list of sample sizes for the two samples.
Counts Python list that is assigned the number of observations in each sample with diameter values less than 2.20.
Python list that is assigned the total number of observations in each sample.
Click the block of code below and hit the Run button above.
from statsmodels.stats.proportion import proportions_ztest
#number of observations in the first sample with diameter values Less than 2.20.
counti len(diameters_sample1_df[diameters_sample1_df["diameters']<2.20])
#number of observations in the second sample with diameter values Less than 2.28.
count2 len(diameters_sample2_df[diameters_sample2_df["diameters']<2.20])
#counts Python List
counts [counti, count2]
#number of observations in the first sample
ni len(diameters_sample1_df)
#number of observations in the second sample
n2 len(diameters_sample2_df)
#n Python List
n = [1, 2]
#perform the hypothesis test. output is a Python tuple that contains test_statistic and the two-sided P_value.
test_statistic, p_value proportions_ztest(counts, n)
print("test-statistic =*, round(test_statistic, 2))
print("two tailed p-value=", round(p_value,4))
test-statistic = 8.69
two tailed p-value - 0.4884
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