欢乐MBA-t检验（标准差σ未知）第九章

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9.74 A bank branch located in a commercial district of a cityhad the business objective of improving the process for serv-ing customers during the noon-to-1:00 P.M. lunch period. Thewaiting time (defined as the time the customer enters the lineuntil he or she reaches the teller window) of a random sampleof 15 customers is collected, and the results are organized(and stored in ) as follows:

4.21 5.55 3.02 5.13 4.77 2.34 3.54 3.204.50 6.10 0.38 5.12 6.46 6.19 3.79


a. At the 0.05 level of significance, is there evidence thatthe population mean waiting time is less than 5 minutes?b. What assumption about the population distribution isneeded in order to conduct the t test in (a)?c. Construct a boxplot or a normal probability plot to evalu-ate the assumption made in (b).d. Do you think that the assumption needed in order to con-duct the t test in (a) is valid? Explain.e. As a customer walks into the branch office during thelunch hour, she asks the branch manager how long shecan expect to wait. The branch manager replies, “Almostcertainly not longer than 5 minutes.” On the basis of theresults of (a), evaluate this statement.
Solution a：

1.       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

Since-1.676718>-1.7613, we cannot reject H0, whichmeans we cannot draw the conclusion that waiting time is less than 5 mins.

σ is unknown andassume the population you are sampling from follows a normal distribution.

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关键词：t检验 标准差 significance distribution Probability