7

# Given values

mean_a = 1000

std_a = 100

n_a = 30

mean_b = 950

std_b = 120

n_b = 30

# Step 1: Compute the difference in means

mean_diff = mean_a - mean_b

# Step 2: Compute the standard error (Welch's formula for unequal variances)

se = ((std_a ** 2) / n_a + (std_b ** 2) / n_b) ** 0.5

# Step 3: Compute the t-statistic

t_stat = mean_diff / se

# Step 4: Compute degrees of freedom using Welch–Satterthwaite approximation

df_numerator = ((std_a ** 2) / n_a + (std_b ** 2) / n_b) ** 2

df_denominator = (( (std_a ** 2) / n_a ) ** 2) / (n_a - 1) + (( (std_b ** 2) / n_b ) ** 2) / (n_b -

1)

df = df_numerator / df_denominator

# Print results

print(f"T-statistic: {t_stat:.4f}")

print(f"Approximate Degrees of Freedom: {df:.2f}")

# Interpretation guide (manual comparison needed)

# For example: Critical t-value at df ≈ 55, α=0.05 (two-tailed) ≈ ±2.004

# Decision

if abs(t_stat) > 2.004:

    print("Result: Reject H₀ → Significant difference in sales.")

else:

    print("Result: Fail to reject H₀ → No significant difference in sales.")