QUESTION 5. [12 marks] A small hotel asks each of its guests to complete a satisfaction survey. One of the questions asks, "How would you rate the cleanliness of your hotel room?" In 2020, the percentages of guests who answered "excellent", "very good", "good", "fair" and "poor" were found to be 5 percent, 12 percent, 25 percent, 37 percent, and 21 percent, respectively. The hotel manager was unsatisfied with these results and decided to retrain the cleaning staff in January 2021 to improve customer satisfaction. To assess the effectiveness of these retraining efforts, the hotel manager took a random sample of 420 guests' answers to the same survey question during February of 2021. The resulting frequencies are recorded in the table below. Excellent Very Good Good Fair Poor 24 58 157 142 39 (a) At a = 0.05, does the distribution of answers to this survey question in the February of this year differ from the distribution of answers last year? Conduct an appropriate test using the critical value method. (b) Based on the result of part (a), do you think the retraining efforts were effective? Answer this question by describing the nature of the differences using the two comparisons of observed and expected frequencies that contributed the greatest to the value of the test statistic. (c) Comment on the validity of the test result in (a)