Survey on hotel guest satisfaction

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Four hotels took part in a survey on hotel guest satisfaction. A follow up question was asked of all respondents who were dissatisfied with the service. These guests were asked to indicate the main reason for their dissatisfaction. You are asked to investigate whether the choice of hotel has any bearing on the main reason for dissatisfaction.
Do not use Excel in this question! Write your answers on paper, showing full working.
(a) State appropriate hypotheses that could be tested to answer the question: “Do the results of the survey provide evidence that the nature of dissatisfaction and the choice of hotel are related?”
(b) A contingency table, summarizing the results of the survey, is given below. The table shows the observed frequencies for each cell, as well as some of the expected frequencies under H0 (in parentheses). Copy down this table, and without using Excel, calculate the remaining expected frequencies under H0. Show working!
Hotel
Fijian Tradeswest Sheraton Coral Reef Totals
Politeness 23 ( ) 7 ( ) 37 (33.7410) 67 (62.0192) 134
Knowledge 25 ( ) 13 ( ) 25 (30.9712) 60 (56.9281) 123
Responsiveness 13 (11.0024) 5 (6.6906) 13 (15.6115) 31 (28.6954) 62
Other 13 (17.3909) 20 (10.5755) 30 (24.6763) 35 (45.3573) 98
Totals 74 45 105 193 417
(c) Write down an expression for the relevant test statistic, and state its distribution under H0(together with any associated parameters!).
(d) Without using Excel, calculate the contribution from the upper-left cell to the observed value of the test statistic.
(e) Given that the observed value of the test statistic is ­2
obs = 20.8059, carry out the test (with-out using Excel) at the 5% significance level, and state your conclusion. Is there sufficient evidence to conclude that there is a relationship between the choice of hotel and the nature of
dissatisfaction?

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