【Python】第七天:区间估计入门!手把手教你算总体均值的置信区间,附 代码

Pythonimport numpy as npimport scipy.statsfrom scipy import stats as sts# 通用函数：计算总体均值的置信区间def mean_conf_interval(data, confidence_coef=0.95):"""data：你的样本数据confidence_coef：置信水平，默认95%，不用改return：置信区间下限、上限"""n = len(data) # 样本量mean = np.mean(data) # 样本均值std = sts.tstd(data, ddof=1) # 样本标准差alpha = 1 - confidence_coef # 显著性水平# 自动判断用z分布还是t分布if n >= 30:# 大样本用z分布score = scipy.stats.norm.isf(alpha / 2)print(f"大样本，使用z分布，临界值：{score:.2f}")else:# 小样本用t分布score = scipy.stats.t.isf(alpha / 2, df = n-1)print(f"小样本，使用t分布，临界值：{score:.2f}")# 计算边际误差和置信区间me = score * std / np.sqrt(n)lower_limit = mean - meupper_limit = mean + mereturn round(lower_limit, 2), round(upper_limit, 2)

Python# 1. 样本数据：20名患者的住院天数hospital_days = [4,6,7,5,8,10,6,7,5,9,3,5,8,6,7,4,11,6,7,8]# 2. 调用函数，计算置信区间conf_interval = mean_conf_interval(hospital_days)mean_days = np.mean(hospital_days)# 3. 打印结果+大白话解读print(f"✅ 样本平均住院天数：{mean_days:.2f}天")print(f"✅ 总体均值95%置信区间：{conf_interval}")print(f"�� 解读：我们有95%的把握，全院内科患者的平均住院天数，在{conf_interval[0]}天到{conf_interval[1]}天之间")

Python# 1. 样本数据：50名用户的消费金额spend_money = [89,159,299,99,199,359,129,259,79,189,69,219,399,119,169,279,89,149,99,229,109,179,249,139,199,329,79,169,119,209,99,189,269,129,219,369,89,159,109,239,119,199,289,149,229,349,99,179,129,219]# 2. 调用函数，计算置信区间conf_interval = mean_conf_interval(spend_money)mean_money = np.mean(spend_money)# 3. 打印结果+大白话解读print(f"✅ 样本平均客单价：{mean_money:.2f}元")print(f"✅ 总体均值95%置信区间：{conf_interval}")print(f"�� 解读：我们有95%的把握，全平台用户的平均客单价，在{conf_interval[0]}元到{conf_interval[1]}元之间")