A bank located in a commercial district of a city has developed an improved proc

Question

 A bank located in a commercial district of a city has developed an improved process for   serving customers during the noon to 1 PM peak lunch period. The waiting time (as   defined as the time the customer enters the line until he or she is served) of all customers   during this hour is recorded over a period of 1 week. A random sample of 15 customers is   selected, and the results are as follows:   4.21, 5.55, 3.02, 5.13, 4.77, 2.34, 3.54, 3.20, 4.50, 6.10, 0.38, 5.12, 6.46, 6.19, 3.79   a) Set up 99% confidence interval for estimating the average waiting time during peak hour.   b) At the 0.01 level Of significance, is there evidence that the average waiting time is less than 5 minutes?   c) Find the p-value for part (b).   d) What assumption must hold in order to perform the test in part (b)? 

Explanation / Answer

from table after solving online weget values as

n=15 , mean = 4.287 std = 1.638 standard error = 0.423

a) 99% CONFIDENCE INTERVAL IS 0.01 FROM Z TABLE ITS VALUE IS 2.977 when df =14

X^+-Za*S.E

4.287+-2.977*0.423

4.287+-1.2592

[ 3.0278      , 5.5462]

b) t= 2.4789

t ctritical = 2.977

tcritc > t so there is sufficient evidence

c) pvalue = 0.00027

d) reject h0 Difference exists between the means

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