t-test with scipy.stats in Data Analysis Python - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of a one-sample t-test

What is the output of this code snippet performing a one-sample t-test?

Data Analysis Python

from scipy import stats
import numpy as np

data = np.array([5, 7, 8, 6, 9])
t_stat, p_value = stats.ttest_1samp(data, popmean=6)
print(round(t_stat, 2), round(p_value, 3))

A 1.87 0.045

B 1.87 0.150

C 1.41 0.222

D 2.24 0.045

💡 Hint

Remember the t-statistic measures how far the sample mean is from the population mean in standard error units.

The t-statistic is about 1.41 and the p-value is approximately 0.222, indicating the sample mean is not significantly different from 6 at 5% level.

❓ data_output

intermediate

Number of significant results in two-sample t-tests

Given two groups of data, how many of the following pairs show a significant difference at alpha=0.05 using independent two-sample t-tests?

Data Analysis Python

from scipy import stats
import numpy as np

pairs = [
    (np.array([10, 12, 11, 13]), np.array([14, 15, 13, 16])),
    (np.array([20, 22, 21, 19]), np.array([18, 17, 20, 16])),
    (np.array([5, 7, 6, 8]), np.array([5, 6, 5, 7]))
]
significant_count = 0
for g1, g2 in pairs:
    t_stat, p_val = stats.ttest_ind(g1, g2)
    if p_val < 0.05:
        significant_count += 1
print(significant_count)

A 2

B 1

C 3

D 0

💡 Hint

Check the p-values for each pair and count how many are below 0.05.

The first two pairs have p-values below 0.05, indicating significant differences. The last pair does not.

🔧 Debug

advanced

Identify the error in paired t-test code

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

Data Analysis Python

from scipy import stats
import numpy as np

before = np.array([100, 102, 98, 101])
after = np.array([102, 105, 100])
t_stat, p_val = stats.ttest_rel(before, after)
print(t_stat, p_val)

A ValueError: operands could not be broadcast together with shapes (4,) (3,)

B TypeError: ttest_rel() missing 1 required positional argument

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

D IndexError: index out of range

💡 Hint

Check if the input arrays have the same length for paired tests.

Paired t-test requires both samples to have the same number of observations. Here, 'before' has 4 and 'after' has 3, causing a broadcasting error.

🧠 Conceptual

advanced

Interpretation of p-value in t-test

If a two-sample t-test returns a p-value of 0.03, what does this mean?

A The alternative hypothesis is true with 97% confidence.

B There is a 3% chance the null hypothesis is true.

C The difference between groups is practically significant.

D There is a 3% chance of observing the data if the null hypothesis is true.

💡 Hint

Remember what p-value measures in hypothesis testing.

The p-value is the probability of observing data as extreme as this, assuming the null hypothesis is true. It is not the probability that the null hypothesis itself is true.

🚀 Application

expert

Choosing the correct t-test for data

You have two sets of exam scores: one from students before a training program and one from the same students after the program. Which t-test should you use to check if the training improved scores?

A Independent two-sample t-test

B Paired t-test

C Welch's t-test

D One-sample t-test

💡 Hint

Think about whether the samples are related or independent.

Since the scores are from the same students before and after training, the samples are paired. A paired t-test accounts for this dependency.