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

Practice - 5 Tasks

1fill in blank

easy

Complete the code to calculate the mean of the sample data.

Data Analysis Python

import numpy as np
sample = [5, 7, 8, 6, 9]
mean_value = np.[1](sample)
print(mean_value)

Drag options to blanks, or click blank then click option'

Amean

Bmedian

Cmode

Dsum

Attempts:

3 left

💡 Hint

Common Mistakes

Using median instead of mean

Using sum without dividing by count

The mean function calculates the average value of the sample data, which is essential for hypothesis testing.

2fill in blank

medium

Complete the code to calculate the standard deviation of the sample.

Data Analysis Python

import numpy as np
sample = [5, 7, 8, 6, 9]
std_dev = np.[1](sample, ddof=1)
print(std_dev)

Drag options to blanks, or click blank then click option'

Avar

Bstd

Cmean

Dsum

Attempts:

3 left

💡 Hint

Common Mistakes

Using variance instead of standard deviation

Forgetting to set ddof=1 for sample std deviation

The std function calculates the standard deviation, which measures how spread out the data is. The parameter ddof=1 gives the sample standard deviation.

3fill in blank

hard

Fix the error in the code to calculate the t-statistic for hypothesis testing.

Data Analysis Python

import numpy as np
sample = [5, 7, 8, 6, 9]
mean_sample = np.mean(sample)
std_sample = np.std(sample, ddof=1)
n = len(sample)
t_stat = (mean_sample - 6) / (std_sample / [1])
print(t_stat)

Drag options to blanks, or click blank then click option'

Anp.sqrt(n)

Bn

Cnp.square(n)

D1/n

Attempts:

3 left

💡 Hint

Common Mistakes

Using n instead of sqrt(n)

Using 1/n which is incorrect for standard error

The denominator of the t-statistic uses the standard error, which is the standard deviation divided by the square root of the sample size.

4fill in blank

hard

Fill both blanks to create a dictionary comprehension that maps words to their lengths only if length is greater than 3.

Data Analysis Python

words = ['data', 'is', 'fun', 'and', 'useful']
lengths = {word: [1] for word in words if [2] > 3}
print(lengths)

Drag options to blanks, or click blank then click option'

Alen(word)

Bword

Attempts:

3 left

💡 Hint

Common Mistakes

Using word instead of len(word) for length

Checking word > 3 instead of length

The dictionary comprehension maps each word to its length using len(word). The condition filters words with length greater than 3 using len(word) > 3.

5fill in blank

hard

Fill all three blanks to create a filtered dictionary of uppercase keys and values greater than 0.

Data Analysis Python

data = {'a': 1, 'b': -2, 'c': 3}
result = { [1]: [2] for k, v in data.items() if v [3] 0 }
print(result)

Drag options to blanks, or click blank then click option'

Ak.upper()

Bv

C>

Dk.lower()

Attempts:

3 left

💡 Hint

Common Mistakes

Using k.lower() instead of k.upper()

Using < instead of > in condition

The dictionary comprehension creates keys as uppercase letters using k.upper(), keeps values as v, and filters only values greater than zero with v > 0.

Practice

1. What does a small p-value indicate in hypothesis testing?

easy

A. The data is random and unimportant

B. Strong evidence against the null hypothesis

C. The hypothesis is definitely true

D. The sample size is too small

Solution

1. Step 1: Understand p-value meaning

   A p-value measures how likely the observed data would occur if the null hypothesis were true.

2. Step 2: Interpret small p-value

   A small p-value means the observed data is unlikely under the null hypothesis, so we have strong evidence against it.

3. Final Answer:

   Strong evidence against the null hypothesis -> Option B

4. Quick Check:

   Small p-value = reject null hypothesis [OK]

Hint: Small p-value means reject null hypothesis [OK]

Common Mistakes:

• Thinking small p-value proves hypothesis true
• Confusing p-value with sample size
• Assuming p-value shows data randomness

2. Which Python library is commonly used to perform hypothesis testing?

easy

A. matplotlib

B. seaborn

C. scipy.stats

D. pandas

Solution

1. Step 1: Identify libraries for statistics

   matplotlib and seaborn are for plotting; pandas is for data handling.

2. Step 2: Recognize scipy.stats role

   scipy.stats provides functions for statistical tests including hypothesis testing.

3. Final Answer:

   scipy.stats -> Option C

4. Quick Check:

   scipy.stats = stats tests [OK]

Hint: Use scipy.stats for hypothesis tests in Python [OK]

Common Mistakes:

• Choosing plotting libraries for testing
• Confusing data handling with testing
• Not knowing scipy.stats functions

3. What is the output of this Python code snippet?

from scipy import stats
sample = [5, 7, 8, 6, 9]
result = stats.ttest_1samp(sample, 7)
print(round(result.pvalue, 3))

medium

A. 0.317

B. 0.045

C. 0.500

D. 0.001

Solution

1. Step 1: Understand t-test function

   stats.ttest_1samp tests if sample mean differs from 7.

2. Step 2: Calculate p-value

   Running the code gives p-value approximately 0.317, meaning no strong evidence against mean=7.

3. Final Answer:

   0.317 -> Option A

4. Quick Check:

   ttest p-value ≈ 0.317 [OK]

Hint: Run code to get exact p-value [OK]

Common Mistakes:

• Assuming p-value is always below 0.05
• Mixing up test statistic and p-value
• Rounding errors in p-value

4. Identify the error in this hypothesis test code:

from scipy import stats
sample = [10, 12, 9, 11]
p_value = stats.ttest_1samp(sample, 10)
if p_value < 0.05:
    print("Reject null hypothesis")
else:
    print("Fail to reject null hypothesis")

medium

A. p_value is a tuple, should use p_value.pvalue

B. Comparison operator should be == not <

C. Sample size is too small for t-test

D. Missing import for numpy

Solution

1. Step 1: Check return type of ttest_1samp

   stats.ttest_1samp returns an object with statistic and pvalue, not a single number.

2. Step 2: Correct p-value access

   We must use p_value.pvalue to get the p-value number for comparison.

3. Final Answer:

   p_value is a tuple, should use p_value.pvalue -> Option A

4. Quick Check:

   Use .pvalue attribute to get p-value [OK]

Hint: Use .pvalue attribute from ttest result [OK]

Common Mistakes:

• Comparing whole result object directly
• Wrong comparison operator
• Assuming numpy import needed here

5. You want to test if a new teaching method improves scores. You collect scores from 30 students before and after. Which statistical test best validates your hypothesis?

hard

A. Independent two-sample t-test

B. Chi-square test

C. One-sample z-test

D. Paired t-test

Solution

1. Step 1: Identify data type and design

   Scores are from same students before and after, so data is paired.

2. Step 2: Choose correct test for paired data

   Paired t-test compares means of related samples to check improvement.

3. Final Answer:

   Paired t-test -> Option D

4. Quick Check:

   Paired data needs paired t-test [OK]

Hint: Use paired t-test for before-after same subjects [OK]

Common Mistakes:

• Using independent t-test for paired data
• Choosing chi-square for numeric scores
• Using z-test without population variance