T检验步骤

Set as below:

H0 is time μ≥ 5 min

H1 is time μ<5 min

2.       Sample size n=15，α=0.05，df=14

3.       σ is unknown，choose t test

4.       For α=0.05, the critical Zvalues are ±1.96

5.       μ=5

x-bar=4.29

S=1.64

tSTAT=(x-bar-μ)/(S/(n)^(1/2))=(x-bar-miu)/s除以根号n=((4.29-5)*(15)^(1/2))/1.64=-1.676718

6.       check on the criticalvalue of t, df=14，α=0.05（单尾查α即可），tα=1.7613

stata用法：

invttail(df,p)

       Description:  the inverse reverse cumulative (upper tail or survivor)

                     Student's t distribution: if ttail(df,t) = p, then

                     invttail(df,p) = t

       Domain df:    2e-10 to 2e+17 (may be nonintegral)

       Domain p:     0 to 1

       Range:        -8e+307 to 8e+307

即：

. di invttail(14,0.05)

1.7613101