Question

A manager for a hotel chain would like to determine if a new process for checking in customers will enable hotel staff to more quickly process check-in's especially during high volume conference dates. Eight entry desk staff were randomly selected and the time spent for standard check-in processes were measured (both for old process and new process approaches.) The data is shown below (time in minutes on the data). Using an appropriate hypothesis testing method, determine if the data supports at the 1% significance level that the new process should, on average, enable the hotel staff to more quickly complete hotel check-in's.

Old Process	New Process
17	15
22	19
15	16
13	12
19	16
26	22
17	14
13	14

Answer 1

The question says here that we have to test that the the new process on an average should quickly complete the check ins compared to the old process meaning that Average time taken by the hotel staff with the new process should be less that Average time taken by the hotel staff with the old process

let x denotes the time taken by the old process

y denotes the time taken by the new process

Then,

H0:µx=µy vs H1:µx>µy

here the sample variance are not equal

the test statistic under H0 is given by

follows, at least approximately, a tr distribution where r, the adjusted degrees of freedom is determined by the equation:

then by computation

=1.75/1.94=0.90

and the adjusted degrees of freedom is given by

which is approximately equal to 12

t value with 12 degrees of freedom at 0.01 level of significance for a one tailed test is 2.68

here the calculated T value is 0.90<2.68 therefore we accept the null hypothesis that there is no difference between the old process or new process

therefore the data does not support the fact that the new process is more efficient than the old one