Question: A hotel measures the overall satisfaction of its guests on a scale of 1 to 7 , where 7 is the most satisfied. Since the hotel's inception, the known mean quality is 6.2 and the known standard deviation is 1.25. After a new hotel manager takes over, a random sample of 91 customers have a sample mean satisfaction rating of 6.5. The CEO of the hotel chain wants to evaluate if the population mean ratings under the new hotel manager are any different than the historical values. Use a Type I error rate of .05.

1. What is/are the critical value(s) for the test of the null hypothesis?
2. (2 points) What is the value of the test statistic in this situation?
3. For your above noted test statistic, what is the \(p\) -value for the test of the null hypothesis

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