Fitting a normal distribution

When working with relatively small data sets you often don't have enough data to make principled inference. However, if you suspect the data follows a normal distribution, it may be reasonable to fit a normal distribution and work with this, rather than with the raw data. In this exercise you will work the same data on Hispanic firefighters which you previously showed was normally distributed at the 5% level. You will fit a normal distribution to it, and use this to find the percentage of these employees we would generally expect to have less than 10 years of experience.

This DataFrame has been loaded for you in salary_df. The packages pandas as pd, NumPy as np, Matplotlib as plt, and the stats package from SciPy have all been loaded for you.

This exercise is part of the course

Foundations of Inference in Python

Exercise instructions

Fit a normal distribution to the Years of Employment column and save the resulting mean and standard deviation.
Use this mean and standard deviation in a normal CDF to estimate the percentage of employees with less than ten years of experience.
Print out this percentage.

Hands-on interactive exercise

Have a go at this exercise by completing this sample code.

# Fit a normal distribution to the data
mu, std = ____

# Compute the percentage of employees with less than 10 years experience
percent = stats.____(____, loc=____, scale=____)

# Print out this percentage
____

Edit and Run Code

This exercise is part of the course

Foundations of Inference in Python

AdvancedSkill Level

4.9+

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In this chapter, we'll explore the relationship between samples and statistically justifiable conclusions. Choosing a sample is the basis of making sound statistical decisions, and we’ll explore how the choice of a sample affects the outcome of your inference.

Exercise 1: Statistical inference and random sampling Exercise 2: Sampling and point estimates Exercise 3: Repeated sampling, point estimates and inference Exercise 4: Sampling and bias Exercise 5: Visualizing samples Exercise 6: Inference and bias Exercise 7: Confidence intervals and sampling Exercise 8: Normal sampling distributions Exercise 9: Calculating confidence intervals Exercise 10: Drawing conclusions from samples

Learn all about applying normality tests, correlation tests, and parametric and non-parametric tests for sound inference. Hypothesis tests are tools, and choosing the right tool for the job is critical for statistical decision-making. While you may be familiar with some of these tests in introductory courses, you'll go deeper to enhance your inferential toolkit in this chapter.

Exercise 1: Normality tests Exercise 2: Testing for normality Exercise 3: Distribution of errors Exercise 4: Fitting a normal distribution

Current Exercise

Exercise 5: Correlation tests Exercise 6: Testing for correlation Exercise 7: Autocorrelation Exercise 8: Explained variance Exercise 9: Parametric tests Exercise 10: Equal variance Exercise 11: Normality of groups Exercise 12: ANOVA Exercise 13: Non-parametric tests Exercise 14: Comparing rankings Exercise 15: Comparing medians

In this chapter, you'll measure and interpret effect size in various situations, encounter the multiple comparisons problem, and explore the power of a test in depth. While p-values tell you if a significant effect is present, they don't tell you how strong that effect is. Effect size measures how strong an effect a treatment has. Master the factors underpinning effect size in this chapter.

Exercise 1: Effect size Exercise 2: Effect size for means Exercise 3: Effect size for correlations Exercise 4: Effect size for categorical variables Exercise 5: Multiple comparisons and corrections Exercise 6: Multiple comparisons problem Exercise 7: Bonferonni-Holm correction Exercise 8: Power of a test Exercise 9: What is power anyway?Exercise 10: Power for experimental design Exercise 11: Computing power and sample sizes

You’ll expand your inferential statistics toolkit further with a look at bootstrapping, permutation tests, and methods of combining evidence from p-values. Bootstrapping will provide you with a first look at statistical simulation. In the lesson meta-analysis, you’ll learn all about combining results from multiple studies. You’ll end with a look at permutation tests, a powerful and flexible non-parametric statistical tool.

Exercise 1: Bootstrapping Exercise 2: Bootstrap confidence intervals Exercise 3: Bootstrapping vs. normality Exercise 4: Combining evidence from p-values Exercise 5: Fisher's method in SciPy Exercise 6: Inference using Fisher's method Exercise 7: Summarizing Fisher's method Exercise 8: Permutation tests Exercise 9: Permutation tests for correlations Exercise 10: Permutation tests and bootstrapping Exercise 11: Analyzing skewed data with a permutation test Exercise 12: Course wrap-up video