5. A researcher conducts an experiment with a sample of 20 participants to determine if a new drug affects heart rate. The sample has a mean heart rate increase of 8 beats per minute and a standard deviation of 2 beats per minute. Perform a hypothesis test using the t-distribution to determine if the mean heart rate increase is significantly different from zero at the 5% significance level.
PROGRAM:
from scipy import stats
import math
# Given data
sample_mean = 8 # mean heart rate increase
sample_std = 2 # standard deviation
n = 20 # sample size
alpha = 0.05 # significance level
# Calculate t-statistic
t_stat = sample_mean / (sample_std / math.sqrt(n))
# Degrees of freedom
df = n - 1
# Two-tailed p-value
p_value = 2 * (1 - stats.t.cdf(abs(t_stat), df=df))
# Print results
print(f"T-statistic: {t_stat:.3f}")
print(f"P-value: {p_value:.5f}")
# Conclusion
if p_value < alpha:
print("Reject the null hypothesis: The mean heart rate increase is significantly different from zero.")
else:
print("Fail to reject the null hypothesis: No significant difference from zero.")OUTPUT:
T-statistic: 17.889
P-value: 0.00000
Reject the null hypothesis: The mean heart rate increase is significantly different from zero.