5

 import scipy.stats as stats

# Given data

sample_mean = 8

sample_std = 2

n = 20

mu = 0 # Hypothesized population mean

# Calculate the t-statistic

t_statistic = (sample_mean - mu) / (sample_std / (n ** 0.5))

# Degrees of freedom

df = n - 1

# Two-tailed p-value

p_value = 2 * (1 - stats.t.cdf(abs(t_statistic), df=df))

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

print(f"Degrees of freedom: {df}")

print(f"P-value: {p_value:.4f}")

# Conclusion

if p_value < 0.05:

print("Result: Reject the null hypothesis. The increase is statistically significant.")

else:

print("Result: Fail to reject the null hypothesis. The increase is not statistically significant.")