11. A bakery claims that its new cookie recipe is lower in calories compared to the old recipe, which had a mean calorie count of 200. You sample 40 new cookies and find a mean of 190 calories with a standard deviation of 15 calories. Perform a one-tailed t-test to determine if the new recipe has significantly fewer calories at a 5% significance level.
PROGRAM:
from scipy import stats
import math
# Given data
old_mean = 200 # mean calories of old recipe
sample_mean = 190 # mean calories of new recipe
sample_std = 15 # standard deviation of new recipe
n = 40 # sample size
alpha = 0.05 # significance level
# Calculate t-statistic
t_stat = (sample_mean - old_mean) / (sample_std / math.sqrt(n))
# Degrees of freedom
df = n - 1
# One-tailed p-value (testing if new mean < old mean)
p_value = stats.t.cdf(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 new recipe has significantly fewer calories.")
else:
print("Fail to reject the null hypothesis: No significant difference in calories.")OUTPUT:
T-statistic: -4.216
P-value: 0.00007
Reject the null hypothesis: The new recipe has significantly fewer calories.