Why statistics validates hypotheses in Data Analysis Python - Challenge Your Understanding

Challenge - 5 Problems

🧠 Conceptual

intermediate

Understanding Hypothesis Testing Purpose

Why do we use statistics to validate hypotheses in data science?

A To randomly select data points for analysis

B To ignore data variability and focus only on averages

C To measure the likelihood that observed data could happen if the hypothesis is false

D To prove the hypothesis is absolutely true without any doubt

💡 Hint

Think about what statistics tells us about data and hypotheses.

Statistics helps us understand how likely our observed data would be if the hypothesis were not true. It does not prove absolute truth but measures evidence strength.

❓ Predict Output

intermediate

Output of p-value calculation

What is the output of this Python code that calculates a p-value for a sample mean?

Data Analysis Python

import scipy.stats as stats
sample_mean = 105
population_mean = 100
std_dev = 15
sample_size = 30
z_score = (sample_mean - population_mean) / (std_dev / (sample_size ** 0.5))
p_value = 2 * (1 - stats.norm.cdf(abs(z_score)))
print(round(p_value, 4))

A 0.0910

B 0.0455

C 0.9545

D 0.1820

💡 Hint

Calculate z-score first, then find two-tailed p-value.

The z-score is about 1.8257, so the two-tailed p-value is approximately 0.0455, indicating significance at 5% level.

❓ data_output

advanced

Result of Hypothesis Test on Sample Data

Given this sample data and a population mean of 50, what is the p-value from a one-sample t-test?

Data Analysis Python

import scipy.stats as stats
sample = [52, 48, 51, 49, 53, 47, 50, 54, 46, 55]
population_mean = 50
t_stat, p_value = stats.ttest_1samp(sample, population_mean)
print(round(p_value, 4))

A 0.0543

B 0.1234

C 0.9876

D 0.0027

💡 Hint

Use the t-test formula for one sample against population mean.

The t-test compares sample mean to population mean; the p-value of 0.0543 suggests borderline significance.

🔧 Debug

advanced

Identify the error in hypothesis test code

What error will this code raise when running a t-test?

Data Analysis Python

import scipy.stats as stats
sample = [5, 7, 8, 6, 9]
pop_mean = 7
result = stats.ttest_1samp(sample, pop_mean)
print(result.pvalue)

A AttributeError: 'tuple' object has no attribute 'pvalue'

B SyntaxError: invalid syntax

C TypeError: ttest_1samp() missing 1 required positional argument

D No error, prints the p-value

💡 Hint

Check what ttest_1samp returns and how to access p-value.

stats.ttest_1samp returns a tuple (statistic, pvalue), so accessing result.pvalue causes AttributeError.

🚀 Application

expert

Choosing correct hypothesis test for data

You have two independent groups with small sample sizes and unknown population variances. Which test should you use to validate if their means differ?

A Chi-square test

B Two-sample t-test assuming equal variances

C Paired t-test

D Two-sample t-test with Welch's correction

💡 Hint

Consider variance equality and sample independence.

Welch's t-test does not assume equal variances and is suitable for small samples with unknown variances.