Question

Use the link in the Jupyter Notebook activity to access your Python script. Once you have made your calculations, complete this discussion. The script will output answers to the questions given below. You must attach your Python script output as an HTML file and respond to the questions below.

In this discussion, you will apply the statistical concepts and techniques covered in this week's reading about hypothesis testing for the difference between two population proportions. In the previous week’s discussion, you studied a manufacturing process at a factory that produces ball bearings for automotive manufacturers. The factory wanted to estimate the average diameter of a particular type of ball bearing to ensure that it was being manufactured to the factory’s specifications.

Recently, the factory began a new production line that is more efficient than the existing production line. However, the factory still needs ball bearings to meet the same specifications. To compare the accuracy of the new process against the existing process, the factory decides to take two random samples of ball bearings. The first sample is of 50 randomly selected ball bearings from the existing production line, and the second sample is of 50 randomly selected ball bearings produced from the new production line. For each sample, the diameters of the ball bearings were measured.

The two samples will be generated using Python’s numpy module. These data sets will be unique to you, and therefore your answers will be unique as well. Run Step 1 in the Python script to generate your unique sample data.

Suppose that the factory claims that the proportion of ball bearings with diameter values less than 2.20 cm in the existing manufacturing process is the same as the proportion in the new process. At alpha=0.05, is there enough evidence that the two proportions are the same? Perform a hypothesis test for the difference between two population proportions to test this claim.

1. Define the null and alternative hypotheses in mathematical terms as well as in words.
2. Identify the level of significance.
3. 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.)
4. Provide a conclusion and interpretation of the test: Should the null hypothesis be rejected? Why or why not
   
   
   Click the block of code below and hit the Run button above. In [1]: 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_sample1 = np.random.normal(2.48,0.500,50) # convert the array into a dataframe with the column name "diameters" using pandas Library diameters_sample1_df = pd.DataFrame (diameters_sample1, 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=0.750) diameters_sample2 = np.random.normal(2.50,0.750,50) # convert the array into a dataframe with the column name "diameters" using pandas Library diameters_sample2_df = pd.DataFrame (diameters_sample2, columns=['diameters']) 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 a) 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 1.91 1 2.34 2 3.03 3 2.26 2.39 4 Diameters data frame of the second sample (showing only the first five observations) diameters 0 2.85 1 2.78 2 2.77 3 2.73 4 1.71
   

Answer 1

As you have executed the code cell. It throws tou an error about diameters_sample1_df is not defined.

You may be able to see that

 ['diameters']<2.20

its showing in blue color thats because python is unable to identify that blue text. This is because you are reffering to that column in wrong way.

The code which you have written is

 count1 = len(diameters_sample1_df[diameters_sample1_df['diameters']<2.20])

This code looks perfectly fine.

And also you should not apply the len function here. Try doing like this:

 count1 = diameters_sample1_df['diameters']<2.20] count1 = len(count1)

These all are different ways you can rectify your error. But still you should give a try this code to run in sequence mean first initialization/declaration/creation and then use it.

Try using small abbrevation variable names.

And most important thing, execute a code in each different cell. It will help you debug you errors. So that will be easy to detect where your error lies.

I recommend you to execute codes in one cell each. Don't just write all your code in one single cell.