P-values and significance in Data Analysis Python - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to calculate the p-value from a t-test.

Data Analysis Python

from scipy import stats
sample1 = [5, 6, 7, 8, 9]
sample2 = [5, 5, 6, 7, 8]
t_stat, p_value = stats.ttest_ind(sample1, sample2)
print('P-value:', [1])

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

Asample1

Bp_value

Ct_stat

Dstats

Attempts:

3 left

💡 Hint

Common Mistakes

Using the t-statistic instead of the p-value.

Printing the function instead of the variable.

The p-value is the second value returned by ttest_ind. It tells us the probability of observing the data if the null hypothesis is true.

2fill in blank

medium

Complete the code to check if the p-value is less than the significance level 0.05.

Data Analysis Python

p_value = 0.03
if p_value [1] 0.05:
    print('Reject the null hypothesis')
else:
    print('Fail to reject the null hypothesis')

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

A<

B>=

C==

D>

Attempts:

3 left

💡 Hint

Common Mistakes

Using > instead of < for the comparison.

Checking equality instead of less than.

If the p-value is less than 0.05, we reject the null hypothesis, meaning the result is statistically significant.

3fill in blank

hard

Fix the error in the code to correctly calculate the p-value for a paired t-test.

Data Analysis Python

from scipy import stats
before = [20, 21, 19, 22, 20]
after = [22, 23, 20, 24, 21]
t_stat, p_value = stats.ttest_rel(before, [1])
print('P-value:', p_value)

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

Aafter

Bstats

Cbefore

Dttest_rel

Attempts:

3 left

💡 Hint

Common Mistakes

Passing the same sample twice.

Passing the function name instead of data.

The paired t-test compares two related samples. The second argument should be the 'after' sample.

4fill in blank

hard

Fill both blanks to create a dictionary of words and their lengths, but only include words longer than 3 letters.

Data Analysis Python

words = ['apple', 'cat', 'banana', 'dog', 'pear']
lengths = { [1]: len([2]) for word in words if len(word) > 3 }

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

Aword

Bwords

Dlen

Attempts:

3 left

💡 Hint

Common Mistakes

Using the list 'words' instead of the variable 'word'.

Using 'len' as a key instead of the word.

The dictionary comprehension uses 'word' as the key and calculates the length of 'word' as the value.

5fill in blank

hard

Fill all three blanks to create a dictionary of uppercase words and their lengths, including only words with length greater than 4.

Data Analysis Python

words = ['apple', 'cat', 'banana', 'dog', 'pear']
result = { [1]: [2] for word in words if len(word) [3] 4 }

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

Aword.upper()

Blen(word)

C>

Dword

Attempts:

3 left

💡 Hint

Common Mistakes

Using the original word instead of uppercase.

Using wrong comparison operator.

The dictionary comprehension uses the uppercase version of the word as the key, the length as the value, and filters words longer than 4 letters.

Practice

1. What does a p-value less than 0.05 usually indicate in a hypothesis test?

easy

A. The results are statistically significant and unlikely due to chance.

B. The results are definitely caused by random chance.

C. The sample size is too small to draw conclusions.

D. The test was performed incorrectly.

Solution

1. Step 1: Understand the meaning of p-value

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

2. Step 2: Compare p-value to significance level

   If the p-value is less than 0.05 (common threshold), it means the observed result is unlikely due to chance, so we reject the null hypothesis.

3. Final Answer:

   The results are statistically significant and unlikely due to chance. -> Option A

4. Quick Check:

   p-value < 0.05 means significant [OK]

Hint: p-value < 0.05 means strong evidence against chance [OK]

Common Mistakes:

• Thinking p-value shows probability null is true
• Confusing significance level with p-value
• Assuming p-value proves practical importance

2. Which of the following is the correct way to check if a p-value stored in variable p_val is significant at 0.05 level in Python?

easy

A. if p_val == 0.05: print('Significant')

B. if p_val > 0.05: print('Significant')

C. if p_val < 0.05: print('Significant')

D. if p_val <= 0.5: print('Significant')

Solution

1. Step 1: Recall significance condition

   A p-value less than 0.05 means significance, so we check if p_val < 0.05.

2. Step 2: Match condition to code

   if p_val < 0.05: print('Significant') uses < 0.05 correctly. Others check wrong conditions or wrong thresholds.

3. Final Answer:

   if p_val < 0.05: print('Significant') -> Option C

4. Quick Check:

   Use < 0.05 for significance [OK]

Hint: Check if p_val < 0.05 for significance [OK]

Common Mistakes:

• Using > instead of < for significance
• Checking equality to 0.05 exactly
• Using wrong threshold like 0.5

3. Given this Python code snippet, what will be printed?

p_val = 0.07
if p_val < 0.05:
    print('Reject null hypothesis')
else:
    print('Fail to reject null hypothesis')

medium

A. Reject null hypothesis

B. SyntaxError

C. No output

D. Fail to reject null hypothesis

Solution

1. Step 1: Check the p-value against 0.05

   The p_val is 0.07, which is greater than 0.05, so the condition p_val < 0.05 is False.

2. Step 2: Determine which branch runs

   Since the condition is False, the else block runs, printing 'Fail to reject null hypothesis'.

3. Final Answer:

   Fail to reject null hypothesis -> Option D

4. Quick Check:

   p_val = 0.07 > 0.05 means fail to reject [OK]

Hint: p_val > 0.05 means fail to reject null [OK]

Common Mistakes:

• Confusing greater than with less than
• Assuming equality means reject
• Ignoring else branch

4. This code is intended to print 'Significant' if p-value is less than 0.05, but it always prints 'Not Significant'. What is the error?

p_val = 0.03
if p_val > 0.05:
    print('Significant')
else:
    print('Not Significant')

medium

A. The comparison operator should be '<' instead of '>'

B. The variable p_val is not defined

C. The print statements are reversed

D. The p_val value is incorrect

Solution

1. Step 1: Analyze the condition logic

   The code checks if p_val > 0.05 to print 'Significant', but significance means p_val < 0.05.

2. Step 2: Identify the fix

   Changing the operator to < will correctly print 'Significant' when p_val is 0.03.

3. Final Answer:

   The comparison operator should be '<' instead of '>' -> Option A

4. Quick Check:

   Use < 0.05 for significance check [OK]

Hint: Use '<' to check p-value significance [OK]

Common Mistakes:

• Using '>' instead of '<' for significance
• Swapping print statements without fixing condition
• Assuming variable is undefined

5. You run a test and get a p-value of 0.049. You want to be very strict and use a significance level of 0.01. What should you conclude?

hard

A. Reject the null hypothesis because 0.049 < 0.05

B. Fail to reject the null hypothesis because 0.049 > 0.01

C. Reject the null hypothesis because 0.049 < 0.01

D. Fail to reject the null hypothesis because 0.049 > 0.05

Solution

1. Step 1: Understand significance level

   The significance level is set to 0.01, meaning p-values must be less than 0.01 to reject the null hypothesis.

2. Step 2: Compare p-value to significance level

   The p-value 0.049 is greater than 0.01, so we fail to reject the null hypothesis at this stricter level.

3. Final Answer:

   Fail to reject the null hypothesis because 0.049 > 0.01 -> Option B

4. Quick Check:

   p-value > significance level means fail to reject [OK]

Hint: Compare p-value to chosen significance level carefully [OK]

Common Mistakes:

• Using default 0.05 without checking chosen level
• Confusing less than and greater than
• Ignoring stricter significance level