t-test (ttest_ind, ttest_rel) in SciPy - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of independent t-test on two samples

What is the output of the following code snippet that performs an independent t-test between two groups?

SciPy

from scipy.stats import ttest_ind
import numpy as np
np.random.seed(0)
group1 = np.random.normal(10, 2, 30)
group2 = np.random.normal(12, 2, 30)
result = ttest_ind(group1, group2)
print((round(result.statistic, 2), round(result.pvalue, 3)))

A (0.45, 0.655)

B (4.03, 0.000)

C (-4.03, 0.000)

D (-0.45, 0.655)

💡 Hint

Remember that ttest_ind returns a statistic and p-value. The sign of the statistic depends on which group mean is larger.

The independent t-test compares means of two independent samples. Since group2 has a higher mean, the t-statistic is negative. The p-value is very small, indicating a significant difference.

❓ data_output

intermediate

Number of significant paired differences

Given the paired samples below, how many pairs show a significant difference at alpha=0.05 using a paired t-test?

SciPy

from scipy.stats import ttest_rel
import numpy as np
np.random.seed(1)
before = np.array([20, 22, 19, 24, 30, 28, 25, 27])
after = np.array([21, 23, 18, 25, 29, 30, 26, 28])
result = ttest_rel(before, after)
print((round(result.statistic, 3), round(result.pvalue, 3)))

A Statistic: -1.414, p-value: 0.197

B Statistic: 1.414, p-value: 0.197

C Statistic: -2.828, p-value: 0.025

D Statistic: 2.828, p-value: 0.025

💡 Hint

Paired t-test compares means of differences. The sign depends on which sample is larger on average.

The paired t-test statistic is negative because the 'before' values are slightly greater than 'after' values on average. The p-value is above 0.05, so differences are not significant.

🔧 Debug

advanced

Identify the error in t-test code

What error will this code raise when run?

SciPy

from scipy.stats import ttest_ind
import numpy as np
a = np.array([1, 2, 3])
b = np.array([4, 5])
result = ttest_ind(a, b)
print(result)

A TypeError: unsupported operand type(s) for -: 'int' and 'str'

B ValueError: operands could not be broadcast together

C IndexError: index out of bounds

D No error, outputs t-statistic and p-value

💡 Hint

Check if ttest_ind requires equal length arrays.

ttest_ind works with arrays of different lengths because it compares independent samples. No error occurs.

🧠 Conceptual

advanced

Choosing between ttest_ind and ttest_rel

Which situation correctly describes when to use ttest_rel instead of ttest_ind?

A Comparing test scores of students before and after a training program

B Comparing heights of men and women in a population

C Comparing sales of two different stores in different cities

D Comparing average temperatures of two different months

💡 Hint

ttest_rel is for paired or related samples.

ttest_rel is used when samples are related or paired, like measurements before and after treatment on the same subjects.

🚀 Application

expert

Interpreting t-test results for clinical trial data

A clinical trial measures blood pressure before and after treatment for 15 patients. The paired t-test returns statistic=3.25 and p-value=0.006. What is the correct interpretation?

A There is no significant change in blood pressure because p-value is greater than 0.01.

B The treatment caused a significant change in blood pressure (p < 0.05), so we reject the null hypothesis.

C The treatment has no effect because the t-statistic is positive.

D The sample size is too small to conclude anything from the test.

💡 Hint

Check the p-value against common significance levels.

A p-value of 0.006 is less than 0.05, indicating a statistically significant difference. The positive t-statistic shows the direction of change.