## A drug-manufacturing company developed a new medicine for cancers, and gave the new medicine to 400 cancer patients.

### statistics

##### Description

A drug-manufacturing company developed a new medicine for cancers, and gave the new medicine to 400 cancer patients. Let Xi be the change of the size of cancer of i-th patient after the administration. Let μ denote the population mean of Xi, namely, E(Xi) = μ. The sample mean of Xi, i =1,…,100, was – 10 mm (millimeter). The sample standard deviation was 10 mm. Let σ 2 denote the population variance of Xi. Let ˆ denote the sample mean.

8) (6 points) Conduct the hypothesis testing for H0: μ = 0 against H1: μ < 0 at significance level α = 0.1, 0.05, and 0.01 with a test statistic constructed by substituting appropriate values into the correct answer for Zn in (7). You can assume that the central limit theorem holds even when unknow parameter(s) in the standardized value is(are) replaced with their consistent estimator(s) (and this is actually true).