import numpy as np import math #sample data data = [8.18, 8.21,8.17,8.22,8.16,8.16,8.17,8.19,8.15,8.18] sample_mean = round(np.mean(data),3) n = len(data) pop_mean_hyp = 8.2 print("Sample mean is {}".format(sample_mean))

def sample_std_dev(data_set): '''Calculates denominator s1 in sample std. dev. formula''' sample_mean = np.mean(data_set) s1 = 0 for i in data: s1 += (i-sample_mean)**2 return s1 s1 = sample_std_dev(data) s = round(math.sqrt(s1/(n-1)),5) print("Sample Std. Dev. using formula is {}".format(s))

alpha = .05 dof = n-1 import scipy.stats t_table = round(scipy.stats.t.ppf(q=alpha/2,df=dof),3) print("t table value is {}".format(t_table)) t_critical = round((sample_mean - pop_mean_hyp)/(s/math.sqrt(n)),3) print(f"t critical value is {t_critical}") p_value = scipy.stats.t.sf(abs(t_critical),df=dof) p_value = round(p_value*2,5) print(f"The p-value is {p_value}") print(f"{p_value} <= {alpha}") if p_value <= alpha: print("Reject Null Hypothesis") else: print("Fail to Reject Null Hypothesis")

CI1 = round(sample_mean - abs(t_table*(s/math.sqrt(n))),3) CI2 = round(sample_mean + abs(t_table*(s/math.sqrt(n))),3) print("The confidence interval for 95% is [{}, {}]".format(CI1,CI2))