3. Suppose you are the manager of a restaurant, and that you have two new employ

Question

3. Suppose you are the manager of a restaurant, and that you have two new employees, Piper and Preston. You are trying to decide where to place them, either as a server or in the kitchen, so you try them in both positions, and record some data on two variables. Data on i of Dshes x-bar 0.766 0.6517 0285 0.6112 13 Data on Tine to Make Entrée (n minutes) Enplovee x-bar Presion24 The employee who drops the fewest dishes is the one that you want to be a server. Use the data on the number of dishes dropped per night to answer the following questions A) Calculate the pooled variance for the difference in the number of dishes dropped per night. B) Use a hypothesis test to conclusively determine who drops fewer plates with a confidence level of 95%. The employee who is the fastest at preparing entrees is the one that you want to work in the kitchen. Use the data on the time it takes for them to make an entrée to answer the following questions. C) Calculate the pooled variance for the difference in average time to make an entrée. D) Conduct a hypothesis test to determine who is faster at making entrees with a confidence level of 95%. E) Who will you make a server, and who will you place in the kitchen? Justify your answer using the information gained from problems 1 and 2.

Explanation / Answer

(A) the pooled variance is calculated as

sp2=((n1-1)s12+(n2-1)s22)/n =0.4

(B)

here we use t-test with null hypothesis H0:mean1=mean2 and alternate hypothesis H1:mean1mean2

statistic t=(mean1-mean2)/((sp*(1/n1 +1/n2)1/2) = 2.01 and

sp2=((n1-1)s12+(n2-1)s22)/n and with df is n=n1+n2-2

two tailed p-value=0.0544 is more than given typical value of alpha=0.05

alpha=(1-0.95)=( 1-confidencelevel)=0.05, so we fail to reject the null hypothesis and conclude that both piper and pretson are statistially same.

(C) same as in part A

pooled variance=7.69

(D) since two tailed p-value=0.0031 is less than typical value of alpha=0.05, we fail to accept H0 and conclude that Pretson is taking more time than Piper. so Piper is faster.

(E) since Piper is faster than Pretson, so piper should be used as server

following information has been generated

sample mean s s2 n (n-1)s2 Piper 0.766 0.6517 0.42471289 13 5.09655468 Preston 0.285 0.6112 0.37356544 15 5.22991616 sum= 28 10.32647084 sp2= 0.40

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